#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; } bool operator==(ModInt that) const { return x == that.x; } bool operator!=(ModInt that) const { return x != that.x; } ModInt operator-() const { ModInt t; t.x = x == 0 ? 0 : Mod - x; return t; } }; template ModInt operator^(ModInt a, unsigned long long k) { ModInt r = 1; while(k) { if(k & 1) r *= a; a *= a; k >>= 1; } return r; } typedef ModInt<1000000007> mint; #pragma region for precomputing int berlekampMassey(const vector &s, vector &C) { int N = (int)s.size(); C.assign(N + 1, mint()); vector B(N + 1, mint()); C[0] = B[0] = 1; int degB = 0; vector T; int L = 0, m = 1; mint b = 1; for(int n = 0; n < N; ++ n) { mint d = s[n]; for(int i = 1; i <= L; ++ i) d += C[i] * s[n - i]; if(d == mint()) { ++ m; } else { if(2 * L <= n) T.assign(C.begin(), C.begin() + (L + 1)); mint coeff = -d * b.inverse(); for(int i = 0; i <= degB; ++ i) C[m + i] += coeff * B[i]; if(2 * L <= n) { L = n + 1 - L; B.swap(T); degB = (int)B.size() - 1; b = d; m = 1; } else { ++ m; } } } C.resize(L + 1); return L; } void computeMinimumPolynomialForLinearlyRecurrentSequence(const vector &a, vector &phi) { int n2 = (int)a.size(), n = n2 / 2; assert(n2 % 2 == 0); int L = berlekampMassey(a, phi); reverse(phi.begin(), phi.begin() + (L + 1)); } #pragma endregion mint linearlyRecurrentSequenceValue(long long K, const vector &initValues, const vector &annPoly) { assert(K >= 0); if(K < (int)initValues.size()) return initValues[(int)K]; int d = (int)annPoly.size() - 1; assert(d >= 0); assert(annPoly[d].get() == 1); assert(d <= (int)initValues.size()); if(d == 0) return mint(); vector coeffs(d), square; coeffs[0] = 1; int l = 0; while((K >> l) > 1) ++ l; for(; l >= 0; -- l) { square.assign(d * 2 - 1, mint()); for(int i = 0; i < d; ++ i) for(int j = 0; j < d; ++ j) square[i + j] += coeffs[i] * coeffs[j]; for(int i = d * 2 - 2; i >= d; -- i) { mint c = square[i]; if(c.x == 0) continue; for(int j = 0; j < d; ++ j) square[i - d + j] -= c * annPoly[j]; } for(int i = 0; i < d; ++ i) coeffs[i] = square[i]; if(K >> l & 1) { mint lc = coeffs[d - 1]; for(int i = d - 1; i >= 1; -- i) coeffs[i] = coeffs[i - 1] - lc * annPoly[i]; coeffs[0] = mint() - lc * annPoly[0]; } } mint res; for(int i = 0; i < d; ++ i) res += coeffs[i] * initValues[i]; return res; } mint linearlyRecurrentSequenceValue(long long K, const pair, vector > &seqPair) { return linearlyRecurrentSequenceValue(K, seqPair.first, seqPair.second); } int main() { int n; long long c; while(~scanf("%d%lld", &n, &c)) { vector as(n); for(int i = 0; i < n; ++ i) scanf("%d", &as[i]); vector dp(n * 2); dp[0] = 1; rep(i, n) { mint a = as[i]; rep(j, (int)dp.size() - 1) dp[j + 1] += dp[j] * a; } vector phi; computeMinimumPolynomialForLinearlyRecurrentSequence(dp, phi); mint ans = linearlyRecurrentSequenceValue(c, dp, phi); rep(i, n) ans -= mint(as[i]) ^ c; printf("%d\n", ans.get()); } return 0; }