import std.stdio, std.array, std.string, std.conv, std.algorithm; import std.typecons, std.range, std.random, std.math, std.container; import std.numeric, std.bigint, core.bitop; immutable long MOD = 10^^9 + 7; int N; long K; long[] A, B; long[][] matmul(int N, long[][] m1, long[][] m2) { auto ret = new long[][](N, N); foreach (i; 0..N) { foreach (j; 0..N) { ret[i][j] = 0; foreach (k; 0..N) { (ret[i][j] += m1[i][k] * m2[k][j] % MOD) %= MOD; } } } return ret; } long[][] matpow(int N, long K, long[][] mat) { auto ret = new long[][](N, N); foreach (i; 0..N) foreach (j; 0..N) ret[i][j] = i == j ? 1 : 0; while (K > 0) { if (K % 2 == 1) ret = matmul(N, ret, mat); mat = matmul(N, mat, mat); K /= 2; } return ret; } void solve1() { // N <= 30 auto F_mat = new long[][](N, N); foreach (i; 0..N) foreach (j; 0..N) F_mat[i][j] = (i == 0 || i == j+1) ? 1 : 0; F_mat = matpow(N, K-N, F_mat); long F = 0; foreach (i; 0..N) (F += F_mat[0][i] * A[$-i-1] % MOD) %= MOD; auto S_mat = new long[][](N+1, N+1); foreach (i; 0..N+1) foreach (j; 0..N+1) { if (i == 0 && j == 0) S_mat[i][j] = 2; else if (i == 0 && j == N) S_mat[i][j] = -1; else if (i == j+1) S_mat[i][j] = 1; else S_mat[i][j] = 0; } S_mat = matpow(N+1, K-N, S_mat); long S = 0; foreach (i; 0..N+1) (S += S_mat[0][i] * B[$-i-1] % MOD) %= MOD; writeln(F, " ", S>=0 ? S:MOD+S); } void solve2() { auto F = new long[](K.to!int+1); F[N] = 0; foreach (i; 0..N) { F[i] = A[i]; (F[N] += A[i] % MOD) %= MOD; } foreach (i; N+1..K.to!int) F[i] = (F[i-1] - F[i-N-1] + F[i-1]) % MOD; long S = 0; foreach (i; 0..K.to!int) S = (S + F[i]) % MOD; writeln(F[K.to!int-1], " ", S); } void main() { auto s = readln.split; N = s[0].to!int; K = s[1].to!long; A = readln.split.map!(to!long).array; B = new long[](N+1); B[0] = 0; foreach (i; 0..N) B[i+1] = B[i] + A[i]; N <= 30 ? solve1 : solve2; //solve2; }