/** * date : 2020-10-16 22:18:56 */ #pragma region kyopro_template #define Nyaan_template #include #include #define pb push_back #define eb emplace_back #define fi first #define se second #define each(x, v) for (auto &x : v) #define all(v) (v).begin(), (v).end() #define sz(v) ((int)(v).size()) #define mem(a, val) memset(a, val, sizeof(a)) #define ini(...) \ int __VA_ARGS__; \ in(__VA_ARGS__) #define inl(...) \ long long __VA_ARGS__; \ in(__VA_ARGS__) #define ins(...) \ string __VA_ARGS__; \ in(__VA_ARGS__) #define inc(...) \ char __VA_ARGS__; \ in(__VA_ARGS__) #define in2(s, t) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i]); \ } #define in3(s, t, u) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i]); \ } #define in4(s, t, u, v) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i], v[i]); \ } #define rep(i, N) for (long long i = 0; i < (long long)(N); i++) #define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--) #define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++) #define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--) #define reg(i, a, b) for (long long i = (a); i < (b); i++) #define die(...) \ do { \ out(__VA_ARGS__); \ return; \ } while (0) using namespace std; using ll = long long; template using V = vector; using vi = vector; using vl = vector; using vvi = vector>; using vd = V; using vs = V; using vvl = vector>; using P = pair; using vp = vector

; using pii = pair; using vpi = vector>; constexpr int inf = 1001001001; constexpr long long infLL = (1LL << 61) - 1; template inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template ostream &operator<<(ostream &os, const pair &p) { os << p.first << " " << p.second; return os; } template istream &operator>>(istream &is, pair &p) { is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const vector &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template istream &operator>>(istream &is, vector &v) { for (auto &x : v) is >> x; return is; } void in() {} template void in(T &t, U &... u) { cin >> t; in(u...); } void out() { cout << "\n"; } template void out(const T &t, const U &... u) { cout << t; if (sizeof...(u)) cout << " "; out(u...); } #ifdef NyaanDebug #define trc(...) \ do { \ cerr << #__VA_ARGS__ << " = "; \ dbg_out(__VA_ARGS__); \ } while (0) #define trca(v, N) \ do { \ cerr << #v << " = "; \ array_out(v, N); \ } while (0) #define trcc(v) \ do { \ cerr << #v << " = {"; \ each(x, v) { cerr << " " << x << ","; } \ cerr << "}" << endl; \ } while (0) template void _cout(const T &c) { cerr << c; } void _cout(const int &c) { if (c == 1001001001) cerr << "inf"; else if (c == -1001001001) cerr << "-inf"; else cerr << c; } void _cout(const unsigned int &c) { if (c == 1001001001) cerr << "inf"; else cerr << c; } void _cout(const long long &c) { if (c == 1001001001 || c == (1LL << 61) - 1) cerr << "inf"; else if (c == -1001001001 || c == -((1LL << 61) - 1)) cerr << "-inf"; else cerr << c; } void _cout(const unsigned long long &c) { if (c == 1001001001 || c == (1LL << 61) - 1) cerr << "inf"; else cerr << c; } template void _cout(const pair &p) { cerr << "{ "; _cout(p.fi); cerr << ", "; _cout(p.se); cerr << " } "; } template void _cout(const vector &v) { int s = v.size(); cerr << "{ "; for (int i = 0; i < s; i++) { cerr << (i ? ", " : ""); _cout(v[i]); } cerr << " } "; } template void _cout(const vector> &v) { cerr << "[ "; for (const auto &x : v) { cerr << endl; _cout(x); cerr << ", "; } cerr << endl << " ] "; } void dbg_out() { cerr << endl; } template void dbg_out(const T &t, const U &... u) { _cout(t); if (sizeof...(u)) cerr << ", "; dbg_out(u...); } template void array_out(const T &v, int s) { cerr << "{ "; for (int i = 0; i < s; i++) { cerr << (i ? ", " : ""); _cout(v[i]); } cerr << " } " << endl; } template void array_out(const T &v, int H, int W) { cerr << "[ "; for (int i = 0; i < H; i++) { cerr << (i ? ", " : ""); array_out(v[i], W); } cerr << " ] " << endl; } #else #define trc(...) #define trca(...) #define trcc(...) #endif inline int popcnt(unsigned long long a) { return __builtin_popcountll(a); } inline int lsb(unsigned long long a) { return __builtin_ctzll(a); } inline int msb(unsigned long long a) { return 63 - __builtin_clzll(a); } template inline int getbit(T a, int i) { return (a >> i) & 1; } template inline void setbit(T &a, int i) { a |= (1LL << i); } template inline void delbit(T &a, int i) { a &= ~(1LL << i); } template int lb(const vector &v, const T &a) { return lower_bound(begin(v), end(v), a) - begin(v); } template int ub(const vector &v, const T &a) { return upper_bound(begin(v), end(v), a) - begin(v); } template int btw(T a, T x, T b) { return a <= x && x < b; } template T ceil(T a, U b) { return (a + b - 1) / b; } constexpr long long TEN(int n) { long long ret = 1, x = 10; while (n) { if (n & 1) ret *= x; x *= x; n >>= 1; } return ret; } template vector mkrui(const vector &v) { vector ret(v.size() + 1); for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i]; return ret; }; template vector mkuni(const vector &v) { vector ret(v); sort(ret.begin(), ret.end()); ret.erase(unique(ret.begin(), ret.end()), ret.end()); return ret; } template vector mkord(int N, F f) { vector ord(N); iota(begin(ord), end(ord), 0); sort(begin(ord), end(ord), f); return ord; } template vector mkiota(int N) { vector ret(N); iota(begin(ret), end(ret), 0); return ret; } template vector mkinv(vector &v) { vector inv(v.size()); for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i; return inv; } struct IoSetupNya { IoSetupNya() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7); } } iosetupnya; void solve(); int main() { solve(); } #pragma endregion using namespace std; template struct LazyMontgomeryModInt { using mint = LazyMontgomeryModInt; using i32 = int32_t; using u32 = uint32_t; using u64 = uint64_t; static constexpr u32 get_r() { u32 ret = mod; for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret; return ret; } static constexpr u32 r = get_r(); static constexpr u32 n2 = -u64(mod) % mod; static_assert(r * mod == 1, "invalid, r * mod != 1"); static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30"); static_assert((mod & 1) == 1, "invalid, mod % 2 == 0"); u32 a; constexpr LazyMontgomeryModInt() : a(0) {} constexpr LazyMontgomeryModInt(const int64_t &b) : a(reduce(u64(b % mod + mod) * n2)){}; static constexpr u32 reduce(const u64 &b) { return (b + u64(u32(b) * u32(-r)) * mod) >> 32; } constexpr mint &operator+=(const mint &b) { if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod; return *this; } constexpr mint &operator-=(const mint &b) { if (i32(a -= b.a) < 0) a += 2 * mod; return *this; } constexpr mint &operator*=(const mint &b) { a = reduce(u64(a) * b.a); return *this; } constexpr mint &operator/=(const mint &b) { *this *= b.inverse(); return *this; } constexpr mint operator+(const mint &b) const { return mint(*this) += b; } constexpr mint operator-(const mint &b) const { return mint(*this) -= b; } constexpr mint operator*(const mint &b) const { return mint(*this) *= b; } constexpr mint operator/(const mint &b) const { return mint(*this) /= b; } constexpr bool operator==(const mint &b) const { return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a); } constexpr bool operator!=(const mint &b) const { return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a); } constexpr mint operator-() const { return mint() - mint(*this); } constexpr mint pow(u64 n) const { mint ret(1), mul(*this); while (n > 0) { if (n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } constexpr mint inverse() const { return pow(mod - 2); } friend ostream &operator<<(ostream &os, const mint &b) { return os << b.get(); } friend istream &operator>>(istream &is, mint &b) { int64_t t; is >> t; b = LazyMontgomeryModInt(t); return (is); } constexpr u32 get() const { u32 ret = reduce(a); return ret >= mod ? ret - mod : ret; } static constexpr u32 get_mod() { return mod; } }; using mint = LazyMontgomeryModInt<1000000007>; using namespace std; template struct Binomial { vector fac_, finv_, inv_; Binomial(int MAX = 0) : fac_(MAX + 10), finv_(MAX + 10), inv_(MAX + 10) { assert(T::get_mod() != 0); MAX += 9; fac_[0] = finv_[0] = inv_[0] = 1; for (int i = 1; i <= MAX; i++) fac_[i] = fac_[i - 1] * i; finv_[MAX] = fac_[MAX].inverse(); for (int i = MAX - 1; i > 0; i--) finv_[i] = finv_[i + 1] * (i + 1); for (int i = 1; i <= MAX; i++) inv_[i] = finv_[i] * fac_[i - 1]; } void extend() { int n = fac_.size(); T fac = fac_.back() * n; T inv = (-inv_[T::get_mod() % n]) * (T::get_mod() / n); T finv = finv_.back() * inv; fac_.push_back(fac); finv_.push_back(finv); inv_.push_back(inv); } T fac(int i) { while (i >= (int)fac_.size()) extend(); return fac_[i]; } T finv(int i) { while (i >= (int)finv_.size()) extend(); return finv_[i]; } T inv(int i) { while (i >= (int)inv_.size()) extend(); return inv_[i]; } T C(int n, int r) { if (n < r || r < 0) return T(0); return fac(n) * finv(n - r) * finv(r); } T C_naive(int n, int r) { if (n < r || r < 0) return T(0); T ret = T(1); r = min(r, n - r); for (int i = 1; i <= r; ++i) ret *= inv(i) * (n--); return ret; } T P(int n, int r) { if (n < r || r < 0) return T(0); return fac(n) * finv(n - r); } T H(int n, int r) { if (n < 0 || r < 0) return T(0); return r == 0 ? 1 : C(n + r - 1, r); } }; void solve() { inl(N, K, M); ll NK = min(N, K); V ds(NK + 1); rep1(d, NK) { // K以下で最大のdの約数は? ll n = K / d * d; while (K - n <= NK) { ds[K - n].push_back(d); n -= d; } } Binomial C; V pown(N + 1); pown[0] = 1; mint NN = N; rep1(i, N) pown[i] = pown[i - 1] * NN; if (M == 1) { mint ans = 0; each(d, ds[0]) { if (d > N) break; // d個確定 ans += pown[N - d] * C.P(N - 1, d - 1); } out(ans); return; } vector coeff2(N + 1); rep(i, N + 1) { coeff2[i] = C.P(N - 2, i - 2) * pown[N - i]; } trc(coeff2); auto rui2 = mkrui(coeff2); mint ans = 0; rep1(i, min(N - 1, K)) { if (i == K) { // i点は確定、他は自由 ans += C.P(N - 2, i - 1) * pown[N - i - 1]; break; } // K - iの約数 each(d, ds[i]) { // とりあえずi+1点の登場は確定 // 少なくとも何点要る? int mi = max(0, d - i - 1) + i + 1; // 多くて何点? int ma = min(N - i - 1, d - 1) + i + 1; trc(i, d, mi, ma); assert(mi <= ma); ans += rui2[ma + 1] - rui2[mi]; } } out(ans); }