feat: add sparse on-disk format for presence matrices

The index packing API now accepts a `sparse` parameter to generate `PersistentSparseBitMatrix` files alongside existing dense matrices. The sibling cache automatically detects this format via an `is_multi.prsb` marker file and routes queries identically to the dense variant. A new `--sparse` CLI flag exposes the option, with tests verifying end-to-end pipeline correctness and storage equivalence.

src/obicompactvec/src/bitmatrix/mod.rs

@@ -22,7 +22,7 @@ mod sparse;
 pub use builder::PersistentBitMatrixBuilder;
 pub use packed::pack_bit_matrix;
 pub use persistent::PersistentBitMatrix;
-pub use sparse::{PersistentSparseBitMatrix, PersistentSparseBitMatrixBuilder};
+pub use sparse::{PersistentSparseBitMatrix, PersistentSparseBitMatrixBuilder, pack_sparse_bit_matrix};
 
 pub(crate) use pairwise::{pairwise_matrix, pairwise2_matrix};
 

src/obicompactvec/src/bitmatrix/sparse.rs

@@ -5,7 +5,7 @@
 //! used by any production code path yet — a new type, not a replacement.
 //!
 //! On-disk layout (a directory, mirroring [`super::PersistentBitMatrix`]'s
-//! own directory-of-files convention): `meta.json` plus four components —
+//! own directory-of-files convention): `sparse_meta.json` plus four components —
 //! `is_multi.prsb` (rank-capable flag: singleton row vs. multi-genome
 //! row), `singleton.pfiv` (genome index, one entry per singleton row,
 //! `ceil(log2(n_cols))` bits each), `multi.pfiv` (`dict_id`, one entry per
@@ -33,13 +33,14 @@ use crate::meta::field;
 use crate::rankselect::{PersistentRankSelectBitVec, PersistentRankSelectBitVecBuilder};
 
 use super::PersistentBitMatrix;
+use super::packed::PackedBitMatrix;
 
 fn is_multi_path(dir: &Path) -> PathBuf { dir.join("is_multi.prsb") }
 fn singleton_path(dir: &Path) -> PathBuf { dir.join("singleton.pfiv") }
 fn multi_path(dir: &Path) -> PathBuf { dir.join("multi.pfiv") }
 fn dict_offsets_base(dir: &Path) -> PathBuf { dir.join("dict_offsets") }
 fn dict_values_path(dir: &Path) -> PathBuf { dir.join("dict_values.bin") }
-fn meta_path(dir: &Path) -> PathBuf { dir.join("meta.json") }
+fn meta_path(dir: &Path) -> PathBuf { dir.join("sparse_meta.json") }
 
 struct SparseMeta {
     n: usize,
@@ -53,7 +54,7 @@ impl SparseMeta {
     fn load(dir: &Path) -> io::Result<Self> {
         let s = fs::read_to_string(meta_path(dir))?;
         let get = |name: &str| {
-            field(&s, name).ok_or_else(|| io::Error::new(io::ErrorKind::InvalidData, format!("bad meta.json: missing {name}")))
+            field(&s, name).ok_or_else(|| io::Error::new(io::ErrorKind::InvalidData, format!("bad sparse_meta.json: missing {name}")))
         };
         Ok(Self {
             n: get("n")?,
@@ -370,3 +371,30 @@ impl PersistentSparseBitMatrixBuilder {
         Ok(builder)
     }
 }
+
+/// `pack --sparse`'s entry point: converts a presence directory into the
+/// sparse on-disk format in place, mirroring [`super::pack_bit_matrix`]'s
+/// convention (old-format files removed only after the new format is
+/// fully written, so a crash mid-conversion leaves the previous, still
+/// valid format rather than a half-written one). Idempotent — does
+/// nothing if `is_multi.prsb` already exists. Packs to dense
+/// (`matrix.pbmx`) first via [`super::pack_bit_matrix`] if that hasn't
+/// happened yet, since the dense→sparse transpose (`build_from_dense`)
+/// needs random row access, which only the packed/columnar dense forms
+/// give — not a further reason to keep the dense file around afterward.
+pub fn pack_sparse_bit_matrix(dir: &Path) -> io::Result<()> {
+    if is_multi_path(dir).exists() {
+        return Ok(());
+    }
+
+    let packed_path = dir.join("matrix.pbmx");
+    if !packed_path.exists() {
+        super::pack_bit_matrix(dir)?;
+    }
+
+    let dense = PersistentBitMatrix::Packed(PackedBitMatrix::open(&packed_path)?);
+    PersistentSparseBitMatrixBuilder::build_from_dense(&dense, dir)?.close()?;
+    drop(dense);
+    fs::remove_file(&packed_path)?;
+    Ok(())
+}

src/obicompactvec/src/lib.rs

@@ -19,7 +19,7 @@ pub use bitvec::{BitIter, PersistentBitVec, PersistentBitVecBuilder};
 pub use fixedintvec::{PersistentFixedIntVec, PersistentFixedIntVecBuilder, bit_width_for_range};
 pub use rankselect::{PersistentRankSelectBitVec, PersistentRankSelectBitVecBuilder};
 pub use eliasfano::{EliasFano, EliasFanoBuilder};
-pub use bitmatrix::{PersistentBitMatrix, PersistentBitMatrixBuilder, PersistentSparseBitMatrix, PersistentSparseBitMatrixBuilder, pack_bit_matrix};
+pub use bitmatrix::{PersistentBitMatrix, PersistentBitMatrixBuilder, PersistentSparseBitMatrix, PersistentSparseBitMatrixBuilder, pack_bit_matrix, pack_sparse_bit_matrix};
 pub use builder::PersistentCompactIntVecBuilder;
 pub use colgroup::{ColGroup, FilterMask, MatrixGroupOps, eval_filter_mask};
 pub use intmatrix::{PersistentCompactIntMatrix, PersistentCompactIntMatrixBuilder, pack_compact_int_matrix};

src/obicompactvec/src/traits.rs

@@ -26,6 +26,14 @@ pub trait BinaryMatrix {
     fn fill_sub_matrix(&self, slots: &[usize], out: &mut [Vec<bool>]);
     /// Per-genome k-mer totals.
     fn count_ones(&self) -> Array1<u64>;
+
+    /// Allocating variant of [`fill_sub_matrix`](Self::fill_sub_matrix) —
+    /// provided once here so implementers only need the fill-in-place form.
+    fn sub_matrix(&self, slots: &[usize]) -> Vec<Vec<bool>> {
+        let mut out: Vec<Vec<bool>> = (0..self.n_cols()).map(|_| Vec::new()).collect();
+        self.fill_sub_matrix(slots, &mut out);
+        out
+    }
 }
 
 /// Convert a Jaccard distance matrix (`1 - J`) into a Mash distance matrix, per

src/obikindex/src/index.rs

@@ -122,7 +122,7 @@ impl KmerIndex {
         fs::File::create(output.join(SENTINEL_INDEXED)).map_err(OKIError::Io)?;
         let idx = KmerIndex::open(output)?;
         let t_pack = Stage::start("pack");
-        idx.pack_matrices()?;
+        idx.pack_matrices(false)?;
         rep.push(t_pack.stop());
         Ok(idx)
     }
@@ -274,8 +274,14 @@ impl KmerIndex {
     ///
     /// Reduces per-query file-open overhead from O(n_genomes) to O(1) per partition.
     /// Column files are kept in place; packed files take priority when opening.
-    pub fn pack_matrices(&self) -> OKIResult<()> {
-        use obicompactvec::{pack_bit_matrix, pack_compact_int_matrix};
+    ///
+    /// If `sparse` is set, presence matrices go one step further, from the
+    /// dense `.pbmx` form into `obicompactvec::PersistentSparseBitMatrix`'s
+    /// on-disk format (see `docmd/architecture/siblings.md`) — count
+    /// matrices are unaffected, sparse count matrices aren't implemented
+    /// (see the sparse-matrix design plan's "Explicitly deferred").
+    pub fn pack_matrices(&self, sparse: bool) -> OKIResult<()> {
+        use obicompactvec::{pack_bit_matrix, pack_compact_int_matrix, pack_sparse_bit_matrix};
         use obilayeredmap::meta::PartitionMeta;
 
         let n = self.n_partitions();
@@ -292,7 +298,13 @@ impl KmerIndex {
                     let layer_dir = index_dir.join(format!("layer_{l}"));
                     let presence_dir = layer_dir.join("presence");
                     let counts_dir   = layer_dir.join("counts");
-                    if presence_dir.exists() { pack_bit_matrix(&presence_dir).map_err(OKIError::Io)?; }
+                    if presence_dir.exists() {
+                        if sparse {
+                            pack_sparse_bit_matrix(&presence_dir).map_err(OKIError::Io)?;
+                        } else {
+                            pack_bit_matrix(&presence_dir).map_err(OKIError::Io)?;
+                        }
+                    }
                     if counts_dir.exists()   { pack_compact_int_matrix(&counts_dir).map_err(OKIError::Io)?; }
                 }
                 Ok(())

src/obikindex/src/merge.rs

@@ -249,7 +249,7 @@ impl KmerIndex {
             let pb = spinner("pack");
             pb.set_message("consolidating column files …");
             let dst2 = KmerIndex::open(output)?;
-            dst2.pack_matrices()?;
+            dst2.pack_matrices(false)?;
             pb.finish_and_clear();
             rep.push(t.stop());
         }

src/obikindex/src/select.rs

@@ -118,7 +118,7 @@ impl KmerIndex {
         self.meta.write(&self.root_path)?;
 
         let t_pack = Stage::start("pack");
-        self.pack_matrices()?;
+        self.pack_matrices(false)?;
         rep.push(t_pack.stop());
         Ok(())
     }

src/obikmer/src/cmd/pack/mod.rs

@@ -9,6 +9,14 @@ use tracing::info;
 pub struct PackArgs {
     /// Index directory to pack
     pub index: PathBuf,
+
+    /// Pack presence matrices into the sparse, deduplicated on-disk format
+    /// instead of the dense one — see `docmd/architecture/siblings.md`.
+    /// Smaller and faster for single-row access on real, sparse data;
+    /// column-oriented access (`--metric` distance matrices) is much
+    /// slower on the sparse format.
+    #[arg(long)]
+    pub sparse: bool,
 }
 
 pub fn run(args: PackArgs) {
@@ -33,7 +41,7 @@ pub fn run(args: PackArgs) {
     let mut rep = Reporter::new();
     let t = Stage::start("pack");
 
-    idx.pack_matrices().unwrap_or_else(|e| {
+    idx.pack_matrices(args.sparse).unwrap_or_else(|e| {
         eprintln!("pack error: {e}");
         std::process::exit(1);
     });

src/obikphylo/src/siblings/cache.rs

@@ -1,6 +1,6 @@
 use rayon::prelude::*;
 
-use obicompactvec::{PersistentBitMatrix, PersistentCompactIntMatrix};
+use obicompactvec::{PersistentBitMatrix, PersistentCompactIntMatrix, PersistentSparseBitMatrix};
 use obikpartitionner::KmerPartition;
 use obikseq::CanonicalKmer;
 use obilayeredmap::Layer;
@@ -40,6 +40,13 @@ use super::{olm_to_ok, SiblingAnnex, INDEX_SUBDIR};
 pub(super) enum Mat {
     Count(Layer<PersistentCompactIntMatrix>),
     Presence(Layer<PersistentBitMatrix>),
+    /// Same role as `Presence`, over a layer packed by `pack --sparse`
+    /// (`PersistentSparseBitMatrix`) instead of the dense form — see
+    /// `docmd/architecture/siblings.md`'s sparse-matrix section. Every
+    /// `Mat` method below dispatches to the same `Layer<D>` generic code
+    /// (`D: LayerData`) as `Presence`, so this arm is purely a storage
+    /// choice, not a behavioural difference.
+    SparsePresence(Layer<PersistentSparseBitMatrix>),
 }
 
 impl Mat {
@@ -47,6 +54,7 @@ impl Mat {
         match self {
             Mat::Count(l) => l.find_slot(kmer),
             Mat::Presence(l) => l.find_slot(kmer),
+            Mat::SparsePresence(l) => l.find_slot(kmer),
         }
     }
 
@@ -60,6 +68,7 @@ impl Mat {
         match self {
             Mat::Count(l) => l.index_batch(kmers),
             Mat::Presence(l) => l.index_batch(kmers),
+            Mat::SparsePresence(l) => l.index_batch(kmers),
         }
     }
 
@@ -74,6 +83,7 @@ impl Mat {
         match self {
             Mat::Count(l) => l.iter_minorants_batch(annex, batch_size),
             Mat::Presence(l) => l.iter_minorants_batch(annex, batch_size),
+            Mat::SparsePresence(l) => l.iter_minorants_batch(annex, batch_size),
         }
     }
 
@@ -81,6 +91,7 @@ impl Mat {
         match self {
             Mat::Count(l) => l.n_cols(),
             Mat::Presence(l) => l.n_cols(),
+            Mat::SparsePresence(l) => l.n_cols(),
         }
     }
 
@@ -100,6 +111,7 @@ impl Mat {
     pub(super) fn fill_sub_matrix_carries(&self, slots: &[usize], out: &mut [Vec<bool>]) {
         match self {
             Mat::Presence(l) => l.fill_sub_matrix(slots, out),
+            Mat::SparsePresence(l) => l.fill_sub_matrix(slots, out),
             Mat::Count(l) => {
                 let mut counts: Vec<Vec<u32>> = out.iter().map(|_| Vec::new()).collect();
                 l.fill_sub_matrix(slots, &mut counts);
@@ -145,8 +157,16 @@ impl PartitionCache {
                 for l in 0..meta.n_layers {
                     let layer_dir = index_dir.join(format!("layer_{l}"));
                     let use_counts = with_counts && layer_dir.join("counts").exists();
+                    // `pack --sparse` converts a layer's `presence/` directory
+                    // in place, leaving `is_multi.prsb` as the on-disk marker
+                    // that distinguishes the sparse format
+                    // (`obicompactvec::PersistentSparseBitMatrix`) from the
+                    // dense one — see `bitmatrix/sparse.rs`'s module docs.
+                    let is_sparse = layer_dir.join("presence").join("is_multi.prsb").exists();
                     let mat = if use_counts {
                         Layer::<PersistentCompactIntMatrix>::open(&layer_dir, &meta.mode).ok().map(Mat::Count)
+                    } else if is_sparse {
+                        Layer::<PersistentSparseBitMatrix>::open(&layer_dir, &meta.mode).ok().map(Mat::SparsePresence)
                     } else {
                         Layer::<PersistentBitMatrix>::open(&layer_dir, &meta.mode).ok().map(Mat::Presence)
                     };

src/obikphylo/src/siblings/tests.rs

@@ -148,6 +148,47 @@ fn sibling_annex_one_sibling_each() {
     assert!(!b.is_minorant(), "g2's stored minorant flag should not be set");
 }
 
+#[test]
+fn sibling_annex_works_after_pack_sparse() {
+    // Same fixture as `sibling_annex_one_sibling_each`, but with
+    // `pack --sparse` (`KmerIndex::pack_matrices(true)`) run on the merged
+    // index before building the sibling annex — proves `PartitionCache`'s
+    // sparse-detection (`Mat::SparsePresence`, gated on `presence/
+    // is_multi.prsb`) and the generic `Layer<D>` methods it relies on
+    // actually round-trip through the real build pipeline, not just the
+    // unit-level `Layer<PersistentSparseBitMatrix>` tests in
+    // `obilayeredmap`.
+    let dir = tempdir().unwrap();
+    let g1 = build_single_genome_index(dir.path(), "g1", b"AACCGCTTAAG");
+    let g2 = build_single_genome_index(dir.path(), "g2", b"AACCGGTTAAG");
+    let merged = merge_two(dir.path(), &g1, &g2);
+    merged.pack_matrices(true).expect("pack_matrices(sparse)");
+
+    let index_dir = merged.partition().part_dir(0).join(INDEX_SUBDIR);
+    assert!(
+        index_dir.join("layer_0").join("presence").join("is_multi.prsb").exists(),
+        "pack_matrices(true) must leave the sparse marker file behind"
+    );
+
+    merged.build_sibling_annex().expect("build_sibling_annex");
+
+    let g1_kmer = canonical(b"AACCGCTTAAG");
+    let g2_kmer = canonical(b"AACCGGTTAAG");
+    let expected_mask = FamilyMask::EMPTY.with(1).with(2);
+
+    let a = annex_info_for(&merged, g1_kmer);
+    assert_eq!(a.bits(), expected_mask.bits(), "AACCGCTTAAG");
+    assert_eq!(a.siblings(), 1);
+    assert!(is_minorant(g1_kmer, a, K), "g1 should be the minorant");
+    assert!(a.is_minorant(), "g1's stored minorant flag should be set at build time");
+
+    let b = annex_info_for(&merged, g2_kmer);
+    assert_eq!(b.bits(), expected_mask.bits(), "AACCGGTTAAG");
+    assert_eq!(b.siblings(), 1);
+    assert!(!is_minorant(g2_kmer, b, K), "g2 should not be the minorant");
+    assert!(!b.is_minorant(), "g2's stored minorant flag should not be set");
+}
+
 #[test]
 fn sibling_annex_zero_siblings_when_identical_and_no_variant_exists() {
     // Same k-mer in both genomes, no other genome around to carry a

src/obilayeredmap/src/layer.rs

@@ -3,8 +3,10 @@ use std::fs;
 use std::path::Path;
 
 use obicompactvec::{
+    BinaryMatrix,
     PersistentBitMatrix, PersistentBitMatrixBuilder,
     PersistentCompactIntMatrix, PersistentCompactIntMatrixBuilder,
+    PersistentSparseBitMatrix,
 };
 use obikseq::CanonicalKmer;
 use obiskio::{UnitigFileReader, UnitigFileWriter};
@@ -47,6 +49,14 @@ impl LayerData for PersistentBitMatrix {
     fn read(&self, slot: usize) -> Box<[bool]> { self.row(slot) }
 }
 
+impl LayerData for PersistentSparseBitMatrix {
+    type Item = Box<[bool]>;
+    fn open(layer_dir: &Path) -> OLMResult<Self> {
+        PersistentSparseBitMatrix::open(&layer_dir.join(PRESENCE_DIR)).map_err(OLMError::Io)
+    }
+    fn read(&self, slot: usize) -> Box<[bool]> { self.row(slot) }
+}
+
 // ── Structures ────────────────────────────────────────────────────────────────
 
 pub struct Layer<D: LayerData = ()> {
@@ -223,15 +233,18 @@ impl Layer<PersistentCompactIntMatrix> {
 
 // ── Mode 3 — presence/absence matrix ─────────────────────────────────────────
 
-impl Layer<PersistentBitMatrix> {
-    pub fn append_genome_column(
-        layer_dir: &Path,
-        value_of: impl Fn(usize) -> bool,
-    ) -> OLMResult<()> {
-        PersistentBitMatrix::append_column(&layer_dir.join(PRESENCE_DIR), value_of)
-            .map_err(OLMError::Io)
-    }
-
+// ── Mode 3 — presence/absence matrix, generic over dense/sparse storage ──────
+//
+// `n_cols`/`sub_matrix`/`fill_sub_matrix` are identical in shape for any
+// `D` satisfying `BinaryMatrix` — genuinely generic (not just two
+// near-identical impl blocks) so `Layer<PersistentSparseBitMatrix>` gets
+// them for free, matching `Layer<PersistentBitMatrix>` at the same call
+// sites (see `obikphylo::siblings::cache::Mat`). Construction
+// (`append_genome_column`/`build_presence`) stays `PersistentBitMatrix`-only
+// below: sparse matrices aren't built column-by-column, they're built
+// row-by-row from an already-built dense layer
+// (`PersistentSparseBitMatrixBuilder::build_from_dense`).
+impl<D: LayerData<Item = Box<[bool]>> + BinaryMatrix> Layer<D> {
     /// Number of genome columns in this layer's presence matrix — see
     /// `PersistentBitMatrix::n_cols`'s docs for the `Implicit` mono-genome
     /// special case (always reports `1`, regardless of the index's real
@@ -244,7 +257,9 @@ impl Layer<PersistentBitMatrix> {
     ///
     /// Returns a column-first `Vec<Vec<bool>>`: one inner `Vec` per genome
     /// column, containing the presence bits for the requested slots in order.
-    /// Column access is sequential for cache efficiency.
+    /// Column access is sequential for cache efficiency on the dense
+    /// storage — on sparse storage it's a naive row-by-row decode, see
+    /// `docmd/architecture/siblings.md`'s sparse-matrix section.
     pub fn sub_matrix(&self, slots: &[usize]) -> Vec<Vec<bool>> {
         self.data.sub_matrix(slots)
     }
@@ -258,6 +273,16 @@ impl Layer<PersistentBitMatrix> {
     pub fn fill_sub_matrix(&self, slots: &[usize], out: &mut [Vec<bool>]) {
         self.data.fill_sub_matrix(slots, out)
     }
+}
+
+impl Layer<PersistentBitMatrix> {
+    pub fn append_genome_column(
+        layer_dir: &Path,
+        value_of: impl Fn(usize) -> bool,
+    ) -> OLMResult<()> {
+        PersistentBitMatrix::append_column(&layer_dir.join(PRESENCE_DIR), value_of)
+            .map_err(OLMError::Io)
+    }
 
     pub fn build_presence(
         out_dir: &Path,

src/obilayeredmap/src/tests/layer.rs

@@ -1,5 +1,6 @@
 use super::*;
-use obikseq::{set_k, Kmer, Sequence as _, Unitig};
+use obicompactvec::PersistentSparseBitMatrixBuilder;
+use obikseq::{set_k, Unitig};
 use obiskio::DEFAULT_BLOCK_BITS;
 use tempfile::tempdir;
 
@@ -42,6 +43,61 @@ fn canonical_kmer_iter_matches_reader() {
     assert_eq!(from_iter, from_reader, "CanonicalKmerIter and UnitigFileReader disagree");
 }
 
+// ── Generic `Layer<D>` over dense vs. sparse presence storage ───────────────
+
+#[test]
+fn presence_layer_generic_over_sparse_matches_dense() {
+    // k=4, matching every other test in this crate's binary: `K`/`M` are
+    // process-wide (not thread-local) in test builds — see
+    // `obikseq::params` — so a test using a different k here would race
+    // against `map.rs`'s k=4 tests running concurrently in the same
+    // binary. These three sequences were chosen (randomised search) to
+    // have no shared canonical 4-mer among them, required for `ptr_hash`
+    // MPHF construction (duplicate keys make it panic).
+    set_k(4);
+    let dir = tempdir().unwrap();
+    write_unitigs(dir.path(), &[b"AAATCTA", b"CTTCGCC", b"TGATACG"]);
+    let n_genomes = 3;
+    let mode = IndexMode::Exact;
+
+    // Deterministic, arbitrary presence function — genome `g` carries a
+    // kmer iff `(kmer's raw bits + g)` is even. Doesn't need to be
+    // biologically meaningful, just the same on both sides of the
+    // dense/sparse comparison below.
+    Layer::<PersistentBitMatrix>::build_presence(dir.path(), DEFAULT_BLOCK_BITS, &mode, n_genomes, |kmer, g| {
+        (kmer.raw().wrapping_add(g as u64)) % 2 == 0
+    }).unwrap();
+
+    let dense_layer = Layer::<PersistentBitMatrix>::open(dir.path(), &mode).unwrap();
+    assert!(dense_layer.n_cols() >= 1);
+
+    // Build the sparse form directly into the same `presence/` dir the
+    // dense form already lives in (matches how `pack --sparse` will work:
+    // same directory, distinct filenames — see
+    // `docmd/architecture/siblings.md`'s sparse-matrix section).
+    let dense_matrix = obicompactvec::PersistentBitMatrix::open(dir.path()).unwrap();
+    PersistentSparseBitMatrixBuilder::build_from_dense(&dense_matrix, &dir.path().join(PRESENCE_DIR))
+        .unwrap()
+        .close()
+        .unwrap();
+
+    let sparse_layer = Layer::<PersistentSparseBitMatrix>::open(dir.path(), &mode).unwrap();
+
+    // Same generic methods, same results, different concrete `D`.
+    assert_eq!(dense_layer.n_cols(), sparse_layer.n_cols());
+    let n = dense_layer.n();
+    assert_eq!(n, sparse_layer.n());
+    let slots: Vec<usize> = (0..n).collect();
+    assert_eq!(dense_layer.sub_matrix(&slots), sparse_layer.sub_matrix(&slots));
+
+    // The matrix-agnostic, MPHF-only surface (from the generic
+    // `impl<D: LayerData> Layer<D>`) must also agree: same kmer set,
+    // looked up through either concrete `D`.
+    for kmer in all_canonical_kmers(dir.path()) {
+        assert_eq!(dense_layer.find_slot(kmer), sparse_layer.find_slot(kmer));
+    }
+}
+
 #[test]
 fn enumerate_kmers_is_stable_across_calls() {
     set_k(4);