import java.io.ByteArrayInputStream; import java.io.IOException; import java.io.InputStream; import java.io.PrintWriter; import java.util.Arrays; import java.util.InputMismatchException; public class D { InputStream is; PrintWriter out; String INPUT = ""; void solve() { int n = ni(); long C = nl(); int[] a = na(n); long[] dp = new long[n]; dp[0] = 1; int mod = 1000000007; long[] rets = new long[200]; for(int i = 0;i < 200;i++){ for(int j = n-1;j >= 0;j--){ for(int k = n-1;k > j;k--){ dp[k] += dp[j] * a[k]; dp[k] %= mod; } dp[j] = dp[j] * a[j]; dp[j] %= mod; } rets[i] = Arrays.stream(dp).sum() % mod; } long[] lx = modifiedBerlekampMassey(rets, mod); for(int i = 0;i < lx.length;i++){ lx[i] = (mod-lx[i])%mod; } lx = Arrays.copyOf(lx, lx.length-1); long ret = 0; if(lx.length > 0){ long[] u = lrx(lx, C-1, mod); for(int i = u.length-1;i >= 0;i--){ ret = ret + rets[i] * u[i]; ret %= mod; } } for(int i = 0;i < n;i++){ ret -= pow(a[i], C, mod); } ret %= mod; if(ret < 0)ret += mod; out.println(ret); } public static long[] lrx(long[] co, long n, long mod) { long BIG = (Long.MAX_VALUE - 2L*mod*mod)/mod*mod; int m = co.length; if(m == 1){ long ret = 1; long mul = co[0]; for(;n > 0;n >>>= 1){ if((n&1)==1){ ret = ret * mul % mod; } mul = mul * mul % mod; } return new long[]{ret}; } long[][] m2 = new long[m-1][m]; for(int j = 0;j < m;j++){ m2[0][j] = co[j]; } for(int i = 1;i < m-1;i++){ for(int j = 0;j < m;j++){ long x = m2[i-1][m-1] * co[j]; if(j-1 >= 0)x += m2[i-1][j-1]; m2[i][j] = x % mod; } } long[] ret = new long[m]; ret[0] = 1; long[] temp = new long[2*m]; for(int l = 62;l >= 0;l--){ if(n<<~l<0){ for(int i = 0;i < m;i++)temp[i] = ret[m-1] * co[i]; for(int i = 1;i < m;i++)temp[i] += ret[i-1]; for(int i = 0;i < m;i++)ret[i] = temp[i] % mod; } if(l > 0){ Arrays.fill(temp, 0L); for(int i = 0;i < m;i++){ for(int j = 0;j < m;j++){ temp[i+j] += ret[i] * ret[j]; if(temp[i+j] >= BIG)temp[i+j] -= BIG; } } for(int i = 0;i < 2*m-1;i++)temp[i] %= mod; for(int i = 0;i < m;i++){ long s = temp[i]; for(int j = m;j < 2*m-1;j++){ s += temp[j] * m2[j-m][i]; if(s >= BIG)s -= BIG; } ret[i] = s % mod; } } } return ret; } public static long invl(long a, long mod) { long b = mod; long p = 1, q = 0; while (b > 0) { long c = a / b; long d; d = a; a = b; b = d % b; d = p; p = q; q = d - c * q; } return p < 0 ? p + mod : p; } public static long[] modifiedBerlekampMassey(long[] a, int mod) { assert a.length % 2 == 0; int n = a.length/2; int m = 2*n-1; long[] R0 = new long[2*n+1]; R0[2*n] = 1; long[] R1 = new long[2*n]; for(int i = 0;i < 2*n;i++)R1[i] = a[m-i]; R1 = strip(R1); long[] v0 = {0L}; long[] v1 = {1L}; while(n <= R1.length-1){ long[][] QR = divmod(R0, R1, mod); long[] v = sub(v0, mul(QR[0], v1, mod), mod); v0 = v1; v1 = v; R0 = R1; R1 = QR[1]; } // normalize long z = invl(v1[v1.length-1], mod); for(int i = 0;i < v1.length;i++){ v1[i] = v1[i] * z % mod; } return strip(v1); } public static long[] mul(long[] a, long[] b, int mod) { long[] c = new long[a.length+b.length-1]; for(int i = 0;i < a.length;i++){ for(int j = 0;j < b.length;j++){ c[i+j] += a[i] * b[j]; c[i+j] %= mod; } } return strip(c); } public static long[] sub(long[] a, long[] b, int mod) { long[] c = Arrays.copyOf(a, Math.max(a.length, b.length)); for(int i = 0;i < c.length;i++){ c[i] -= b[i]; if(c[i] < 0)c[i] += mod; } return strip(c); } public static long[] strip(long[] a) { int i; for(i = a.length-1;i > 0 && a[i] == 0;i--); if(i + 1 == a.length)return a; return Arrays.copyOf(a, i+1); } public static long[][] divmod(long[] A, long[] B, int mod) { assert B[B.length-1] != 0; long[] R = Arrays.copyOf(A, A.length); long[] Q = new long[Math.max(1, A.length-B.length+1)]; long ib = invl(B[B.length-1], mod); for(int i = A.length-1, t = Q.length-1;i >= B.length-1;i--,t--){ long m = R[i] * ib % mod; Q[t] = m; for(int j = 0, k = i-B.length+1+j;j < B.length;j++,k++){ R[k] -= B[j] * m; R[k] %= mod; if(R[k] < 0)R[k] += mod; } assert R[i] == 0; } return new long[][]{Q, strip(R)}; } public static long pow(long a, long n, long mod) { // a %= mod; long ret = 1; int x = 63 - Long.numberOfLeadingZeros(n); for (; x >= 0; x--) { ret = ret * ret % mod; if (n << 63 - x < 0) ret = ret * a % mod; } return ret; } void run() throws Exception { is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes()); out = new PrintWriter(System.out); long s = System.currentTimeMillis(); solve(); out.flush(); if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); // Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){ // @Override // public void run() { // long s = System.currentTimeMillis(); // solve(); // out.flush(); // if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); // } // }; // t.start(); // t.join(); } public static void main(String[] args) throws Exception { new D().run(); } private byte[] inbuf = new byte[1024]; public int lenbuf = 0, ptrbuf = 0; private int readByte() { if(lenbuf == -1)throw new InputMismatchException(); if(ptrbuf >= lenbuf){ ptrbuf = 0; try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); } if(lenbuf <= 0)return -1; } return inbuf[ptrbuf++]; } private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); } private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; } private double nd() { return Double.parseDouble(ns()); } private char nc() { return (char)skip(); } private String ns() { int b = skip(); StringBuilder sb = new StringBuilder(); while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ') sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } private char[] ns(int n) { char[] buf = new char[n]; int b = skip(), p = 0; while(p < n && !(isSpaceChar(b))){ buf[p++] = (char)b; b = readByte(); } return n == p ? buf : Arrays.copyOf(buf, p); } private int[] na(int n) { int[] a = new int[n]; for(int i = 0;i < n;i++)a[i] = ni(); return a; } private long[] nal(int n) { long[] a = new long[n]; for(int i = 0;i < n;i++)a[i] = nl(); return a; } private char[][] nm(int n, int m) { char[][] map = new char[n][]; for(int i = 0;i < n;i++)map[i] = ns(m); return map; } private int[][] nmi(int n, int m) { int[][] map = new int[n][]; for(int i = 0;i < n;i++)map[i] = na(m); return map; } private int ni() { return (int)nl(); } private long nl() { long num = 0; int b; boolean minus = false; while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')); if(b == '-'){ minus = true; b = readByte(); } while(true){ if(b >= '0' && b <= '9'){ num = num * 10 + (b - '0'); }else{ return minus ? -num : num; } b = readByte(); } } private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); } }