#include #include #include using namespace std; const int64_t MOD = 1000000007; void next(vector &x, const vector &first, long MOD) { long last = x.back(); for(int i = x.size() - 2; i >= 0 ; i--) x[i + 1] = x[i]; x[0] = 0; if(last == 500000004) last = 333333331; for(int i = 0; i < x.size(); i++) x[i] = (MOD + x[i] - (long)last * first[i] % MOD) % MOD; } vector next2N(const vector &x, const vector &first, long MOD) { vector tmp(x); vector result(x.size()); for(int i = 0; i < x.size(); i++) { for(int j = 0; j < tmp.size(); j++) { result[j] = (result[j] + MOD - x[i] * tmp[j]) % MOD; } next(tmp, first, MOD); } return result; } long calc(const vector &poly, const vector &x, long MOD, int ofs = 0) { __int128_t ret = 0; for(int i = 0; i < poly.size(); i++) { ret += x[i + ofs] * poly[i] % MOD; ret %= MOD; } return (MOD - ret) % MOD; } long kitamasa(const vector &poly, const vector &x, int64_t N, long MOD) { if(N < poly.size()) return x[N]; int t = poly.size(), l = 0; while(t > 0) t >>= 1, l++; for(int i = 0; i <= l; i++) { if(N >> (63 - __builtin_clzl(N) - l + i) & 1) { t |= 1LL << i; } } long cur = poly.size(); vector curPoly = poly; vector poy2 = poly; while(cur < t) { if(cur == N) { return calc(curPoly, x, MOD); } next(curPoly, poly, MOD); cur++; } vector ret(curPoly.size()); cur = 0; for(int i = 63 - __builtin_clzl(N) - l - 1; i >= 0; i--) { curPoly = next2N(curPoly, poly, MOD); if(N >> i & 1) next(curPoly, poly, MOD); } return calc(curPoly, x, MOD); } int main() { int64_t N, K; cin >> N >> K; vector A(N); for(auto &t: A) cin >> t; if(K <= 1000000) { A.push_back(accumulate(A.begin(), A.end(), 0LL) % MOD); while(A.size() < K) { A.push_back((A.back() * 2 + MOD - A[A.size() - N - 1]) % MOD); } cout << A.back() << " " << accumulate(A.begin(), A.end(), 0LL) % MOD << endl; } else { A.push_back(accumulate(A.begin(), A.end(), 0LL) % MOD); while(A.size() < N + 2) { A.push_back((A.back() * 2 + MOD - A[A.size() - N - 1]) % MOD); } vector poly(N, MOD-1), poly2(N + 1, MOD-1), retpoly(N + 2, 0); poly2[N] = 1; // x - 1を掛ける for(int i = 0; i < N + 1; i++) { retpoly[i + 1] += poly2[i]; retpoly[i] = (retpoly[i] + (MOD - 1) * poly2[i]) % MOD; } // x + 1をかける poly2 = retpoly; retpoly = vector(N + 3); for(int i = 0; i < N + 2; i++) { retpoly[i + 1] += poly2[i]; retpoly[i] = (retpoly[i] + poly2[i]) % MOD; } poly2 = retpoly; vector B(A); for(int i = 1; i < N + 2; i++) { B[i] = (B[i - 1] + A[i]) % MOD; } poly2.pop_back(); cout << kitamasa(poly, A, K - 1, MOD) << " " << kitamasa(poly2, B, K - 1, MOD) << endl; } }