#include <bits/stdc++.h>
using namespace std;
const int Mod = 1e9 + 7;
int n, m, u, f[3100][3100], sum[3100][3100], C[3100][3100], inv[3100], g[3100];
int edgenum, vet[210000], Next[210000], Head[110000];
void addedge(int u, int v) {
  vet[++edgenum] = v;
  Next[edgenum] = Head[u];
  Head[u] = edgenum;
}
void dfs(int u) {
  for (int i = Head[u]; i; i = Next[i]) {
    dfs(vet[i]);
    for (int j = 1; j <= n; j++) f[u][j] = 1ll * f[u][j] * sum[vet[i]][j] % Mod;
  }
  for (int i = 1; i <= n; i++) sum[u][i] = (sum[u][i - 1] + f[u][i]) % Mod;
}
int main() {
  scanf("%d%d", &n, &m);
  for (int i = 2; i <= n; i++) {
    scanf("%d", &u);
    addedge(u, i);
  }
  for (int i = 1; i <= n; i++)
    for (int j = 1; j <= n; j++) f[i][j] = 1;
  dfs(1);
  C[0][0] = 1;
  for (int i = 1; i <= n; i++) {
    C[i][0] = 1;
    for (int j = 1; j <= i; j++)
      C[i][j] = (C[i - 1][j] + C[i - 1][j - 1]) % Mod;
  }
  inv[0] = 1;
  inv[1] = 1;
  for (int i = 2; i <= n; i++)
    inv[i] = 1ll * (Mod - Mod / i) * inv[Mod % i] % Mod;
  for (int i = 2; i <= n; i++) inv[i] = 1ll * inv[i - 1] * inv[i] % Mod;
  for (int i = 1; i <= n; i++) {
    g[i] = f[1][i];
    for (int j = 1; j < i; j++)
      g[i] = (g[i] - 1ll * C[i - 1][j - 1] * g[j] % Mod + Mod) % Mod;
  }
  int ans = 0;
  for (int i = 1; i <= n && i <= m; i++) {
    int mul = inv[i];
    for (int j = m - i + 1; j <= m; j++) mul = 1ll * mul * j % Mod;
    ans = (ans + 1ll * mul * g[i] % Mod) % Mod;
  }
  printf("%d\n", ans);
  return 0;
}
