#pragma GCC optimize("O3") #pragma GCC target("avx2") #pragma GCC optimize("unroll-loops") //#pragma GCC optimize ("Ofast") #include #include using namespace std; #define rep(i, n) for (int i = 0; i < (n); ++i) #define FOR(i, m, n) for (int i = (m); i < (n); ++i) #define rrep(i, n) for (int i = (n)-1; i >= 0; --i) #define rfor(i, m, n) for (int i = (m); i >= (n); --i) using ll = long long; #ifdef _WIN32 #define getchar_unlocked _getchar_nolock #define putchar_unlocked _putchar_nolock #define fwrite_unlocked _fwrite_nolock #define fread_unlocked _fread_nolock #endif #if __has_include("dump.hpp") #include "dump.hpp" #else #define dump(...) ((void)0) #endif // #define USE_FREAD #ifdef USE_FREAD struct Input { static constexpr size_t MAX_SIZE = 4400019; char buf[MAX_SIZE]; size_t i, end; Input() { i = 0; end = fread_unlocked(buf, 1, MAX_SIZE, stdin); } inline int gc() { if (i < end) { return buf[i++]; } else { return EOF; } } } in; #define gc in.gc #else #define gc getchar_unlocked #endif // USE_FREAD // #define USE_FWRITE #ifdef USE_FWRITE struct Output { static constexpr size_t MAX_SIZE = 4000009; char buf[MAX_SIZE]; size_t i = 0; void pc(int c) { buf[i++] = c; } ~Output() { fwrite_unlocked(buf, 1, i, stdout); } } out; #define pc out.pc #else #define pc putchar_unlocked #endif // USE_FWRITE inline void ini(int& v) noexcept { v = 0; char c = gc(); bool f = false; if (c == '-') { f = true; c = gc(); } for (; '0' <= c && c <= '9'; c = gc()) v = v * 10 + (c - '0'); if (f) v = -v; } inline void inui(int& v) noexcept { v = 0; for (char c = gc(); '0' <= c && c <= '9'; c = gc()) v = v * 10 + (c - '0'); } inline void inl(ll& v) noexcept { v = 0; char c = gc(); bool f = false; if (c == '-') { f = true; c = gc(); } for (; '0' <= c && c <= '9'; c = gc()) v = v * 10 + (c - '0'); if (f) v = -v; } inline void inul(ll& v) noexcept { v = 0; for (char c = gc(); '0' <= c && c <= '9'; c = gc()) v = v * 10 + (c - '0'); } inline void ins(char* c, int n) noexcept { while (n--) { *c = gc(); ++c; } } inline void puti(int v) noexcept { if (v < 0) pc('-'), v = -v; char b[10]; int n = 0; while (v) b[n++] = '0' + v % 10, v /= 10; if (!n) b[n++] = '0'; while (n--) pc(b[n]); } inline void putui(int v) noexcept { char b[10]; int n = 0; while (v) b[n++] = '0' + v % 10, v /= 10; if (!n) b[n++] = '0'; while (n--) pc(b[n]); } inline void putl(ll v) noexcept { if (v < 0) pc('-'), v = -v; char b[20]; int n = 0; while (v) b[n++] = '0' + v % 10, v /= 10; if (!n) b[n++] = '0'; while (n--) pc(b[n]); } inline void putul(ll v) noexcept { char b[20]; int n = 0; while (v) b[n++] = '0' + v % 10, v /= 10; if (!n) b[n++] = '0'; while (n--) pc(b[n]); } // ---------------------------------------------------------------- // constexpr ll MOD = 1000000007; inline ll Powmod(ll a, ll n) { ll r = 1; while (n > 0) { if (n & 1) r = r * a % MOD, n--; else a = a * a % MOD, n >>= 1; } return r; } int main() { ll n, m, k; inul(n); inul(m); inul(k); ll acc = 1, x = 0; FOR(i, 1, n + 1) { if (k % i == 0) { x = (x + acc * Powmod(n, n - i)) % MOD; } acc = (acc * (n - i)) % MOD; } if (m == 1) { putul(x); } else { putul((Powmod(n, n) - x) * Powmod(n - 1, MOD - 2) % MOD); } pc('\n'); }