diff --git a/tc/include/tc/core.hpp b/tc/include/tc/core.hpp
index 0e9786e..268cb3b 100644
--- a/tc/include/tc/core.hpp
+++ b/tc/include/tc/core.hpp
@@ -10,5 +10,5 @@
 #include "group.hpp"
 
 namespace tc {
-    Cosets solve(const Group &group, const std::vector<Coset> &sub_gens);
+    Cosets solve(const Group &group, const std::vector<Gen> &sub_gens);
 }
diff --git a/tc/include/tc/cosets.hpp b/tc/include/tc/cosets.hpp
index e579cb1..4d59b4b 100644
--- a/tc/include/tc/cosets.hpp
+++ b/tc/include/tc/cosets.hpp
@@ -6,55 +6,67 @@
 
 namespace tc {
     using Coset = uint32_t;
-    using Gen = uint16_t;
+    using Gen = uint8_t;
     using Mult = uint16_t;
-    
+
     using Rel = std::tuple<Gen, Gen, Mult>;
 
     struct Cosets {
-        int ngens;
+        const Coset UNSET = Coset(-1);
+
+        Gen ngens;
         std::vector<int> data;
         Path path;
 
         Cosets(const Cosets &) = default;
 
-        explicit Cosets(int ngens)
+        explicit Cosets(Gen ngens)
             : ngens(ngens) {
         }
 
         void add_row() {
-            data.resize(data.size() + ngens, -1);
+            data.resize(data.size() + ngens, UNSET);
             path.add_row();
         }
 
-        void put(int coset, int gen, int target) {
+        void put(Coset coset, Gen gen, Coset target) {
             data[coset * ngens + gen] = target;
             data[target * ngens + gen] = coset;
 
-            if (path.get(target).from_idx == -1) {
+            if (path.get(target).from_idx == UNSET) {
                 path.put(coset, gen, target);
             }
         }
 
-        void put(int idx, int target) {
-            int coset = idx / ngens;
-            int gen = idx % ngens;
+        void put(size_t idx, Coset target) {
+            Coset coset = idx / ngens;
+            Gen gen = idx % ngens;
+
             data[idx] = target;
             data[target * ngens + gen] = coset;
 
-            if (path.get(target).from_idx == -1) {
+            if (path.get(target).from_idx == UNSET) {
                 path.put(coset, gen, target);
             }
         }
 
-        [[nodiscard]] int get(int coset, int gen) const {
+        [[nodiscard]] Coset get(Coset coset, Gen gen) const {
             return data[coset * ngens + gen];
         }
 
-        [[nodiscard]] int get(int idx) const {
+        [[nodiscard]] Coset get(size_t idx) const {
             return data[idx];
         }
 
+        [[nodiscard]] bool isset(Coset coset, Gen gen) const {
+            return get(coset, gen) != UNSET;
+        }
+
+        [[nodiscard]] bool isset(size_t idx) const {
+            return get(idx) != UNSET;
+        }
+
+
         [[nodiscard]] size_t size() const {
             return path.size();
         }
diff --git a/tc/src/core.cpp b/tc/src/core.cpp
index cf159d9..79943fa 100644
--- a/tc/src/core.cpp
+++ b/tc/src/core.cpp
@@ -40,7 +40,7 @@ namespace tc {
         }
     };
 
-    Cosets solve(const Group &group, const std::vector<Coset> &sub_gens) {
+    Cosets solve(const Group &group, const std::vector<Gen> &sub_gens) {
         auto ngens = group.ngens;
 
         // region Initialize Cosets Table
@@ -75,7 +75,7 @@ namespace tc {
             const auto &[i, j, m] = rel_tables.rels[table_idx];
             Row &row = rel_tables.rows[0][table_idx];
 
-            if (cosets.get(i) + cosets.get(j) == -2) {
+            if (!cosets.isset(0, i) && !cosets.isset(0, j)) {
                 row.lst_idx = lst_vals.size();
                 lst_vals.push_back(0);
                 row.free = false;
@@ -94,7 +94,7 @@ namespace tc {
 
         while (true) {
             // find next unknown product
-            while (idx < cosets.data.size() and cosets.get(idx) >= 0)
+            while (idx < cosets.data.size() and cosets.isset(idx))
                 idx++;
 
             // if there are none, then return
diff --git a/tc/test/test_solve.cpp b/tc/test/test_solve.cpp
index 019c4e2..c6edbe7 100644
--- a/tc/test/test_solve.cpp
+++ b/tc/test/test_solve.cpp
@@ -8,7 +8,12 @@
 int main(int argc, char *argv[]) {
     std::string key = argv[1];
 
-    std::vector<std::tuple<std::string, tc::Group, std::vector<tc::Coset>, size_t>> groups;
+    std::vector<std::tuple<
+        std::string,
+        tc::Group,
+        std::vector<tc::Gen>,
+        size_t
+    >> groups;
 
     // See the group orders here https://en.wikipedia.org/wiki/Coxeter_group#Properties
     if (key == "A") {
diff --git a/tc/test/test_solve_speed.cpp b/tc/test/test_solve_speed.cpp
index 5144c86..80319a6 100644
--- a/tc/test/test_solve_speed.cpp
+++ b/tc/test/test_solve_speed.cpp
@@ -9,7 +9,12 @@ int main(int argc, char *argv[]) {
     std::string key = argv[1];
 
     std::cerr << "Min. cos/s: " << MINIMUM_COS_PER_SEC << std::endl;
-    std::vector<std::tuple<std::string, tc::Group, std::vector<unsigned int>, size_t>> groups;
+    std::vector<std::tuple<
+        std::string,
+        tc::Group,
+        std::vector<tc::Gen>,
+        size_t
+    >> groups;
 
     // See the group orders here https://en.wikipedia.org/wiki/Coxeter_group#Properties
     if (key == "B") {