#include #include #include #include #include #define REP(i, n) for (int i = 0; i < (n); i++) using namespace std; const int MOD = 1e9 + 7; struct mint { int n; mint(int n_ = 0) : n(n_) {} }; mint operator+(mint a, mint b) { a.n += b.n; if (a.n >= MOD) a.n -= MOD; return a; } mint operator-(mint a, mint b) { a.n -= b.n; if (a.n < 0) a.n += MOD; return a; } mint operator*(mint a, mint b) { return (long long)a.n * b.n % MOD; } mint &operator+=(mint &a, mint b) { return a = a + b; } mint &operator-=(mint &a, mint b) { return a = a - b; } mint &operator*=(mint &a, mint b) { return a = a * b; } mint modpow(mint a, long long b) { mint res = 1; while (b > 0) { if (b & 1) res *= a; a *= a; b >>= 1; } return res; } mint F[200001] = {1, 1}; mint R[200001] = {1, 1}; mint I[200001] = {0, 1}; mint C(int n, int r) { if (n < 0 || r < 0 || n < r) return 0; return F[n] * R[n - r] * R[r]; } void init() { for (int i = 2; i <= 200000; i++) { I[i] = I[MOD % i] * (MOD - MOD / i); F[i] = F[i - 1] * i; R[i] = R[i - 1] * I[i]; } } mint modinv(mint a) { return modpow(a, MOD - 2); } template struct FFT { complex rots[N]; FFT() { const double pi = acos(-1); for (int i = 0; i < N / 2; i++) { rots[i + N / 2].real(cos(2 * pi / N * i)); rots[i + N / 2].imag(sin(2 * pi / N * i)); } for (int i = N / 2 - 1; i >= 1; i--) { rots[i] = rots[i * 2]; } } inline complex mul(complex a, complex b) { return complex( a.real() * b.real() - a.imag() * b.imag(), a.real() * b.imag() + a.imag() * b.real() ); } void fft(vector> &a, bool rev) { const int n = a.size(); int i = 0; for (int j = 1; j < n - 1; j++) { for (int k = n >> 1; k > (i ^= k); k >>= 1); if (j < i) { swap(a[i], a[j]); } } for (int i = 1; i < n; i *= 2) { for (int j = 0; j < n; j += i * 2) { for (int k = 0; k < i; k++) { auto s = a[j + k + 0]; auto t = mul(a[j + k + i], rots[i + k]); a[j + k + 0] = s + t; a[j + k + i] = s - t; } } } if (rev) { reverse(a.begin() + 1, a.end()); for (int i = 0; i < n; i++) { a[i] *= 1.0 / n; } } } vector convolution(vector a, vector b) { int t = 1; while (t < a.size() + b.size() - 1) t *= 2; vector> z(t); for (int i = 0; i < a.size(); i++) z[i].real(a[i]); for (int i = 0; i < b.size(); i++) z[i].imag(b[i]); fft(z, false); vector> w(t); for (int i = 0; i < t; i++) { auto p = (z[i] + conj(z[(t - i) % t])) * complex(0.5, 0); auto q = (z[i] - conj(z[(t - i) % t])) * complex(0, -0.5); w[i] = p * q; } fft(w, true); vector ans(a.size() + b.size() - 1); for (int i = 0; i < ans.size(); i++) { ans[i] = round(w[i].real()); } return ans; } vector convolution(vector a, vector b) { int t = 1; while (t < a.size() + b.size() - 1) t *= 2; vector> A(t), B(t); for (int i = 0; i < a.size(); i++) A[i] = complex(a[i].n & 0x7fff, a[i].n >> 15); for (int i = 0; i < b.size(); i++) B[i] = complex(b[i].n & 0x7fff, b[i].n >> 15); fft(A, false); fft(B, false); vector> C(t), D(t); for (int i = 0; i < t; i++) { int j = (t - i) % t; auto AL = (A[i] + conj(A[j])) * complex(0.5, 0); auto AH = (A[i] - conj(A[j])) * complex(0, -0.5); auto BL = (B[i] + conj(B[j])) * complex(0.5, 0); auto BH = (B[i] - conj(B[j])) * complex(0, -0.5); C[i] = AL * BL + AH * BL * complex(0, 1); D[i] = AL * BH + AH * BH * complex(0, 1); } fft(C, true); fft(D, true); vector ans(a.size() + b.size() - 1); for (int i = 0; i < ans.size(); i++) { long long l = (long long)round(C[i].real()) % MOD; long long m = ((long long)round(C[i].imag()) + (long long)round(D[i].real())) % MOD; long long h = (long long)round(D[i].imag()) % MOD; ans[i] = (l + (m << 15) + (h << 30)) % MOD; } return ans; } }; FFT<1 << 21> fft; vector prod(const vector &A, const vector &B, int l, int r) { if (r - l == 1) return {A[l], B[l]}; int m = (l + r) / 2; auto vl = prod(A, B, l, m); auto vr = prod(A, B, m, r); return fft.convolution(vl, vr); } int main() { init(); int N, R; cin >> N >> R; vector S(N); REP(i, N) cin >> S[i]; sort(S.rbegin(), S.rend()); int i = 0; vector A, B; while (i < N) { int j = i; while (i < N && S[i] == S[j]) i++; A.push_back(F[i - j] * C(i-j + j-1, i-j)); B.push_back(F[i - j] * C(i-j-1 + j, j)); } vector f = prod(A, B, 0, A.size()); mint ans = 0; for (int i = 0; i < f.size(); i++) { ans += f[i] * i * modpow(R, i); } cout << ans.n << '\n'; }