#include "bits/stdc++.h" using namespace std; #define rep(i,n) for(int (i)=0;(i)<(int)(n);++(i)) #define rer(i,l,u) for(int (i)=(int)(l);(i)<=(int)(u);++(i)) #define reu(i,l,u) for(int (i)=(int)(l);(i)<(int)(u);++(i)) static const int INF = 0x3f3f3f3f; static const long long INFL = 0x3f3f3f3f3f3f3f3fLL; typedef vector vi; typedef pair pii; typedef vector > vpii; typedef long long ll; template static void amin(T &x, U y) { if (y < x) x = y; } template static void amax(T &x, U y) { if (x < y) x = y; } template struct ModInt { static const int Mod = MOD; unsigned x; ModInt() : x(0) { } ModInt(signed sig) { int sigt = sig % MOD; if (sigt < 0) sigt += MOD; x = sigt; } ModInt(signed long long sig) { int sigt = sig % MOD; if (sigt < 0) sigt += MOD; x = sigt; } int get() const { return (int)x; } ModInt &operator+=(ModInt that) { if ((x += that.x) >= MOD) x -= MOD; return *this; } ModInt &operator-=(ModInt that) { if ((x += MOD - that.x) >= MOD) x -= MOD; return *this; } ModInt &operator*=(ModInt that) { x = (unsigned long long)x * that.x % MOD; return *this; } ModInt &operator/=(ModInt that) { return *this *= that.inverse(); } ModInt operator+(ModInt that) const { return ModInt(*this) += that; } ModInt operator-(ModInt that) const { return ModInt(*this) -= that; } ModInt operator*(ModInt that) const { return ModInt(*this) *= that; } ModInt operator/(ModInt that) const { return ModInt(*this) /= that; } ModInt inverse() const { signed a = x, b = MOD, u = 1, v = 0; while (b) { signed t = a / b; a -= t * b; std::swap(a, b); u -= t * v; std::swap(u, v); } if (u < 0) u += Mod; ModInt res; res.x = (unsigned)u; return res; } }; typedef ModInt<1000000007> mint; vector fact, factinv; void nCr_computeFactinv(int N) { N = min(N, mint::Mod - 1); fact.resize(N + 1); factinv.resize(N + 1); fact[0] = 1; rer(i, 1, N) fact[i] = fact[i - 1] * i; factinv[N] = fact[N].inverse(); for (int i = N; i >= 1; i --) factinv[i - 1] = factinv[i] * i; } mint nCr(int n, int r) { if (n >= mint::Mod) return nCr(n % mint::Mod, r % mint::Mod) * nCr(n / mint::Mod, r / mint::Mod); return r > n ? 0 : fact[n] * factinv[n - r] * factinv[r]; } mint nHr(int n, int r) { return r == 0 ? 1 : nCr(n + r - 1, r); } int main() { int N; int K; int D; while (~scanf("%d%d%d", &N, &K, &D)) { nCr_computeFactinv(N * 2); int num = (N - 1) / (K - 1); int len = N - num * (K - 1); mint ans; if (D == 1) { ans = len; } else { mint pow = 1; for (int j = 1; j <= N; j += K - 1) { int n = (N - j - (len - 1)) / (K - 1); ans += pow * len * nHr(len - 1, n); pow *= D; } } printf("%d\n", ans.get()); } return 0; }