#line 1 "library-cpp/other/template.hpp" // clang-format off #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using uint = unsigned int; using ll = long long; using ull = unsigned long long; using i128 = __int128_t; using ld = long double; using pii = pair; using pll = pair; template using maxheap = priority_queue; template using minheap = priority_queue, greater>; template using vec = vector; template using vvec = vector>; #define OVERLOAD_REP(_1, _2, _3, name, ...) name #define REP0(n) for (auto minato = decay_t{}; minato < (n); ++minato) #define REP1(i, n) for (auto i = decay_t{}; (i) < (n); (i)++) #define REP2(i, l, r) for (auto i = (l); (i) < (r); (i)++) #define rep(...) OVERLOAD_REP(__VA_ARGS__, REP2, REP1, REP0)(__VA_ARGS__) #define OVERLOAD_RREP(_1, _2, _3, name, ...) name #define RREP1(i, n) for (auto i = (n) - 1; (i) >= decay_t{}; (i)--) #define RREP2(i, l, r) for (auto i = (r) - 1; (i) >= (l); (i)--) #define rrep(...) OVERLOAD_RREP(__VA_ARGS__, RREP2, RREP1)(__VA_ARGS__) #define ALL(x) begin(x), end(x) template int SZ(const Container& v) { return int(v.size()); } template void UNIQUE(vector& v) { v.erase(unique(v.begin(), v.end()), v.end()); } template T MAX(const vector& v) { return *max_element(v.begin(), v.end()); } template T MIN(const vector& v) { return *min_element(v.begin(), v.end()); } template T SUM(const vector& v) { return accumulate(v.begin(), v.end(), T(0)); } template T ABS(T x) { return max(x, -x); } template bool chmax(T1& a, T2 b) { if (a < b) { a = b; return true; } return false; } template bool chmin(T1& a, T2 b) { if (a > b) { a = b; return true; } return false; } int topbit(ull x) { return x == 0 ? -1 : 63 - __builtin_clzll(x); } int botbit(ull x) { return x == 0 ? 64 : __builtin_ctzll(x); } int popcount(ull x) { return __builtin_popcountll(x); } int kthbit(ull x, int k) { return (x >> k) & 1; } constexpr long long TEN(int x) { return x == 0 ? 1 : TEN(x - 1) * 10; } template void rearrange(const vector& id) { (void)id; } template void rearrange_exec(const vector& id, vector& v) { vector w(v.size()); for (size_t i = 0; i < id.size(); i++) { w[i] = v[id[i]]; } v.swap(w); } template void rearrange(const vector& id, Head& a, Tail& ...tail) { rearrange_exec(id, a); rearrange(id, tail...); } istream& operator>>(istream& is, __int128_t& x) { x = 0; string s; is >> s; int n = int(s.size()), it = 0; if (s[0] == '-') it++; for (; it < n; it++) x = (x * 10 + s[it] - '0'); if (s[0] == '-') x = -x; return is; } ostream& operator<<(ostream& os, __int128_t x) { if (x == 0) return os << 0; if (x < 0) os << '-', x = -x; deque deq; while (x) deq.emplace_front(x % 10), x /= 10; for (int e : deq) os << e; return os; } template vector &operator++(vector& v) { for (auto& e : v) { e++; } return v;} template vector operator++(vector& v, int) { auto res = v; for (auto& e : v) { e++; } return res; } template vector &operator--(vector& v) { for (auto& e : v) { e--; } return v; } template vector operator--(vector& v, int) { auto res = v; for (auto& e : v) { e--; } return res; } template pair operator-(const pair& x) { return pair(-x.first, -x.second); } template pair operator-(const pair& x, const pair& y) { return pair(x.first - y.first, x.second - y.second); } template pair operator+(const pair& x, const pair& y) { return pair(x.first + y.first, x.second + y.second); } template pair operator+=(pair& l, const pair& r) { return l = l + r; } template pair operator-=(pair& l, const pair& r) { return l = l - r; } constexpr char ln = '\n'; const string YESNO[2] = {"NO", "YES"}; const string YesNo[2] = {"No", "Yes"}; void YES(bool t = true) { cout << YESNO[t] << "\n"; } void NO(bool t = 1) { YES(!t); } void Yes(bool t = true) { cout << YesNo[t] << "\n"; } void No(bool t = 1) { Yes(!t); } template void drop(T x) { cout << x << "\n"; exit(0); } #define INT(...) \ int __VA_ARGS__; \ IN(__VA_ARGS__) #define LL(...) \ ll __VA_ARGS__; \ IN(__VA_ARGS__) #define STR(...) \ string __VA_ARGS__; \ IN(__VA_ARGS__) #define CHR(...) \ char __VA_ARGS__; \ IN(__VA_ARGS__) #define LDB(...) \ long double __VA_ARGS__; \ IN(__VA_ARGS__) #define VEC(type, name, size) \ vector name(size); \ IN(name) #define VEC2(type, name1, name2, size) \ vector name1(size), name2(size); \ for (int i = 0; i < size; i++) IN(name1[i], name2[i]) #define VEC3(type, name1, name2, name3, size) \ vector name1(size), name2(size), name3(size); \ for (int i = 0; i < size; i++) IN(name1[i], name2[i], name3[i]) #define VEC4(type, name1, name2, name3, name4, size) \ vector name1(size), name2(size), name3(size), name4(size); \ for (int i = 0; i < size; i++) IN(name1[i], name2[i], name3[i], name4[i]); #define VV(type, name, N, M) \ vector> name(N, vector(M)); \ IN(name) template void scan(T& a) { cin >> a; } template void scan(vector& a) { for (auto& i : a) scan(i); } void IN() {} template void IN(Head& head, Tail&... tail) { scan(head); IN(tail...); } void print() { cout << "\n"; } template void print(const vector& v) { for (auto it = v.begin(); it != v.end(); ++it) { if (it != v.begin()) { cout << " "; } cout << *it; } print(); } template void print(const T& x, const Args& ... args) { cout << x; if (sizeof...(Args)) cout << " "; print(args...); } #ifdef MINATO_LOCAL template ostream& operator<<(ostream& os, pair p) { return os << "(" << p.first << ", " << p.second << ")"; } template void debug_tuple(ostream& os, TUPLE _) { (void)os; (void)_; } template void debug_tuple(ostream &os, TUPLE t) { os << (N == 0 ? "" : ", ") << get(t); debug_tuple(os, t); } template ostream& operator<<(ostream& os, tuple t) { os << "("; debug_tuple<0, tuple, Args...>(os, t); return os << ")"; } string debug_delim(int& i) { return i++ == 0 ? "" : ", "; } #define debug_embrace(x) { int i = 0; os << "{"; { x } return os << "}"; } template ostream& operator<<(ostream& os, vector v) { debug_embrace( for (T e : v) { os << debug_delim(i) << e; } ) } template ostream& operator<<(ostream& os, array a) { debug_embrace( for (T e : a) { os << debug_delim(i) << e; } ) } template enable_if_t>, ostream>& operator<<(ostream& os, T(&a)[N]) { debug_embrace( for (T e : a) { os << debug_delim(i) << e; } ) } template ostream& operator<<(ostream& os, set s) { debug_embrace( for (Key e : s) { os << debug_delim(i) << e; }) } template ostream& operator<<(ostream& os, map mp) { debug_embrace( for (auto e : mp) { os << debug_delim(i) << e; }) } template ostream& operator<<(ostream& os, multiset s) { debug_embrace( for (Key e : s) { os << debug_delim(i) << e; }) } template ostream& operator<<(ostream& os, queue q) { debug_embrace( for (; !q.empty(); q.pop()) { os << debug_delim(i) << q.front(); } ) } template ostream& operator<<(ostream& os, deque q) { debug_embrace( for (T e : q) { os << debug_delim(i) << e; } ) } template ostream& operator<<(ostream& os, priority_queue q) { debug_embrace( for (; !q.empty(); q.pop()) { os << debug_delim(i) << q.top(); } ) } template ostream& operator<<(ostream& os, priority_queue, greater> q) { debug_embrace( for (; !q.empty(); q.pop()) { os << debug_delim(i) << q.top(); } ) } void debug_out() { cerr << endl; } template void debug_out(const T& x, const Args& ... args) { cerr << " " << x; debug_out(args...); } #define debug(...) cerr << __LINE__ << " : [" << #__VA_ARGS__ << "] =", debug_out(__VA_ARGS__) #else #define debug(...) (void(0)) #endif /////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// // clang-format on #line 2 "library-cpp/mod/ModInt.hpp" #line 2 "library-cpp/other/type_traits.hpp" namespace internal { #ifndef _MSC_VER template using is_signed_int128 = typename std::conditional::value || std::is_same::value, std::true_type, std::false_type>::type; template using is_unsigned_int128 = typename std::conditional::value || std::is_same::value, std::true_type, std::false_type>::type; template using make_unsigned_int128 = typename std::conditional::value, __uint128_t, unsigned __int128>; template using is_integral = typename std::conditional::value || is_signed_int128::value || is_unsigned_int128::value, std::true_type, std::false_type>::type; template using is_signed_int = typename std::conditional<(is_integral::value && std::is_signed::value) || is_signed_int128::value, std::true_type, std::false_type>::type; template using is_unsigned_int = typename std::conditional<(is_integral::value && std::is_unsigned::value) || is_unsigned_int128::value, std::true_type, std::false_type>::type; template using to_unsigned = typename std::conditional< is_signed_int128::value, make_unsigned_int128, typename std::conditional::value, std::make_unsigned, std::common_type>::type>::type; #else template using is_integral = typename std::is_integral; template using is_signed_int = typename std::conditional::value && std::is_signed::value, std::true_type, std::false_type>::type; template using is_unsigned_int = typename std::conditional::value && std::is_unsigned::value, std::true_type, std::false_type>::type; template using to_unsigned = typename std::conditional::value, std::make_unsigned, std::common_type>::type; #endif template using is_signed_int_t = std::enable_if_t::value>; template using is_unsigned_int_t = std::enable_if_t::value>; template using to_unsigned_t = typename to_unsigned::type; } // namespace internal #line 4 "library-cpp/mod/ModInt.hpp" #line 6 "library-cpp/mod/ModInt.hpp" template struct ModInt { public: static constexpr int mod() { return m; } static ModInt raw(int v) { ModInt x; x._v = v; return x; } ModInt() : _v(0) { } template * = nullptr> ModInt(T v) { long long x = (long long)(v % (long long)(umod())); if (x < 0) x += umod(); _v = (unsigned int)(x); } template * = nullptr> ModInt(T v) { _v = (unsigned int)(v % umod()); } unsigned int val() const { return _v; } ModInt& operator++() { _v++; if (_v == umod()) _v = 0; return *this; } ModInt& operator--() { if (_v == 0) _v = umod(); _v--; return *this; } ModInt operator++(int) { ModInt result = *this; ++*this; return result; } ModInt operator--(int) { ModInt result = *this; --*this; return result; } ModInt& operator+=(const ModInt& rhs) { _v += rhs._v; if (_v >= umod()) _v -= umod(); return *this; } ModInt& operator-=(const ModInt& rhs) { _v -= rhs._v; if (_v >= umod()) _v += umod(); return *this; } ModInt& operator*=(const ModInt& rhs) { unsigned long long z = _v; z *= rhs._v; _v = (unsigned int)(z % umod()); return *this; } ModInt& operator^=(long long n) { ModInt x = *this; *this = 1; if (n < 0) x = x.inv(), n = -n; while (n) { if (n & 1) *this *= x; x *= x; n >>= 1; } return *this; } ModInt& operator/=(const ModInt& rhs) { return *this = *this * rhs.inv(); } ModInt operator+() const { return *this; } ModInt operator-() const { return ModInt() - *this; } explicit operator bool() const { return _v != 0; } ModInt pow(long long n) const { ModInt r = *this; r ^= n; return r; } ModInt inv() const { int a = _v, b = umod(), y = 1, z = 0, t; for (;;) { t = a / b; a -= t * b; if (a == 0) { assert(b == 1 || b == -1); return ModInt(b * z); } y -= t * z; t = b / a; b -= t * a; if (b == 0) { assert(a == 1 || a == -1); return ModInt(a * y); } z -= t * y; } } friend ModInt operator+(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) += rhs; } friend ModInt operator-(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) -= rhs; } friend ModInt operator*(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) *= rhs; } friend ModInt operator/(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) /= rhs; } friend ModInt operator^(const ModInt& lhs, long long rhs) { return ModInt(lhs) ^= rhs; } friend bool operator==(const ModInt& lhs, const ModInt& rhs) { return lhs._v == rhs._v; } friend bool operator!=(const ModInt& lhs, const ModInt& rhs) { return lhs._v != rhs._v; } friend ModInt operator+(long long lhs, const ModInt& rhs) { return (ModInt(lhs) += rhs); } friend ModInt operator-(long long lhs, const ModInt& rhs) { return (ModInt(lhs) -= rhs); } friend ModInt operator*(long long lhs, const ModInt& rhs) { return (ModInt(lhs) *= rhs); } friend ostream& operator<<(ostream& os, const ModInt& M) { return os << M._v; } friend istream& operator>>(istream& is, ModInt& M) { long long x; is >> x; M = x; return is; } private: unsigned int _v; static constexpr unsigned int umod() { return m; } }; #line 2 "library-cpp/mod/ModCombination.hpp" #line 5 "library-cpp/mod/ModCombination.hpp" template struct ModCombination { public: ModCombination() { } ModCombination(int n) : n_(n), fac_(n + 1), facinv_(n + 1) { assert(1 <= n); fac_[0] = 1; for (int i = 1; i <= n; i++) fac_[i] = fac_[i - 1] * i; facinv_[n] = M(1) / fac_[n]; for (int i = n; i >= 1; i--) facinv_[i - 1] = facinv_[i] * i; } M fac(int k) const { assert(0 <= k and k <= n_); return fac_[k]; } M facinv(int k) const { assert(0 <= k and k <= n_); return facinv_[k]; } M inv(int k) const { assert(1 <= k and k <= n_); return facinv_[k] * fac_[k - 1]; } M P(int n, int k) const { if (k < 0 or k > n) return M(0); assert(n <= n_); return fac_[n] * facinv_[n - k]; } M C(int n, int k) const { if (k < 0 or k > n) return M(0); assert(n <= n_); return fac_[n] * facinv_[n - k] * facinv_[k]; } /** * @note H(n, k) = (n 個 のボールを k 個の箱に分ける方法の数) * @note H(n, k) = C(n + k - 1, n) */ M H(int n, int k) const { if (n == 0 and k == 0) return M(1); return C(n + k - 1, n); } M catalan(int n) const { if (n == 0) return M(1); return C(2 * n, n) - C(2 * n, n - 1); } private: int n_; std::vector fac_, facinv_; }; #line 4 "A.cpp" using mint = ModInt<998244353>; // using mint = ModInt<1000000007>; void solve() { ModCombination MC(1000000); INT(N, M, K); STR(S); vec masks(N + 1); rep(i, N) { int k = S[i] - 'a'; masks[i + 1] = masks[i] | (1 << k); } vvec dp(27, vec(27)); rep(i, 27) dp[i][i] = 1; auto sm = dp; rep(M - N) { vvec ndp(27, vec(27)); rep(i, 27) rep(j, 27) { ndp[i][j] += dp[i][j] * j; if (j + 1 <= 26) { ndp[i][j + 1] += dp[i][j] * (26 - j); } } swap(dp, ndp); rep(i, 27) rep(j, 27) { sm[i][j] += dp[i][j]; } } mint ans = 0; rrep(i, N) { int s = S[i] - 'a'; int zero = 0, one = 0; rep(k, s) { if (kthbit(masks[i], k)) { zero++; } else { one++; } } int p = popcount(masks[i]); rep(j, K, 27) { ans += sm[p][j] * zero; if (p + 1 <= 26) { ans += sm[p + 1][j] * one; } } if (p >= K) ans++; vvec ndp(27, vec(27)); rep(j, 27) rep(k, 27) { ndp[j][k] += dp[j][k] * k; if (k + 1 <= 26) { ndp[j][k + 1] += dp[j][k] * (26 - k); } } swap(dp, ndp); rep(j, 27) rep(k, 27) { sm[j][k] += dp[j][k]; } } print(ans); } int main() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); cerr << fixed << setprecision(7); int T = 1; // cin >> T; for (int test_case = 1; test_case <= T; test_case++) { // debug(test_case); solve(); } }