#include <bits/stdc++.h>
using namespace std;
template <typename T>
inline void read(T &x) {
  x = 0;
  char c = getchar(), f = 0;
  for (; c < '0' || c > '9'; c = getchar())
    if (c == '-') f = 1;
  for (; c >= '0' && c <= '9'; c = getchar())
    x = (x << 1) + (x << 3) + (c ^ 48);
  if (f) x = -x;
}
const int P = 1e9 + 7;
int n, D, dp[3005][3005], s[3005][3005], res;
struct edge {
  int to, nxt;
} e[3005];
int et, head[3005], iv[3005];
inline int ksm(int x, int q = P - 2) {
  int r = 1;
  for (; q; q >>= 1, x = 1ll * x * x % P)
    if (q & 1) r = 1ll * r * x % P;
  return r;
}
inline void adde(int x, int y) { e[++et] = (edge){y, head[x]}, head[x] = et; }
inline void dfs(int x) {
  for (int i = 1; i <= n + 1; i++) dp[x][i] = 1;
  for (int i = head[x]; i; i = e[i].nxt) {
    dfs(e[i].to);
    for (int j = 1; j <= n + 1; j++)
      dp[x][j] = 1ll * dp[x][j] * s[e[i].to][j] % P;
  }
  for (int i = 1; i <= n + 1; i++) s[x][i] = (s[x][i - 1] + dp[x][i]) % P;
}
inline int inv(int x) { return x < 0 ? P - iv[-x] : iv[x]; }
int main() {
  read(n), read(D);
  for (int i = 2, f; i <= n; i++) read(f), adde(f, i);
  iv[1] = 1;
  for (int i = 2; i <= n + 1; i++) iv[i] = 1ll * iv[P % i] * (P - P / i) % P;
  dfs(1);
  for (int i = 1, w = 1; i <= n + 1;
       (res += 1ll * w * s[1][i] % P) %= P, w = 1, i++)
    for (int j = 1; j <= n + 1; j++)
      if (i ^ j) w = 1ll * w * (D - j) % P * inv(i - j) % P;
  return printf("%d\n", (res + P) % P), 0;
}
