#include <bits/stdc++.h>
using namespace std;
using ll = long long;
constexpr int kMod = 1'000'000'007;

ll kmp2(const vector<int> &f, int c) {
    const int n = (int)f.size() - 1;
    vector<int> a(n), trace;
    vector<bool> vis(n);
    a[0] = 0;
    ll ans = c;
    for (int i = 1, j = 0; i < n;) {
        trace.clear();
        while (j + 1 != f[i + 1]) {
            if (!vis[a[j]]) {
                vis[a[j]] = true;
                trace.push_back(a[j]);
            }
            j = f[j];
        }
        if (j != -1) a[i] = a[j];
        else {
            while (vis[a[i]]) ++a[i];
            ans = ans * (c - trace.size()) % kMod;
        }
        assert(f[++i] == ++j);
        for (int v : trace) vis[v] = false;
    }
    return ans;
}
int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int n, c;
    cin >> n >> c;
    vector<int> f(1 + n);
    f[0] = -1, f[1] = 0;
    for (int i = 2; i <= n; ++i) cin >> f[i];
    cout << kmp2(f, c) << endl;
    return 0;
}