#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const int M = 1e9 + 7;

struct DSU {
    vector<int> f;
    DSU(int n) : f(n + 1) {
        for (int i = 1; i <= n; i++) {
            f[i] = i;
        }
    }
    int getfa(int v) { return f[v] == v ? v : (f[v] = getfa(f[v])); }
    bool merge(int u, int v) {
        u = getfa(u), v = getfa(v);
        if (u == v) {
            return false;
        }
        f[u] = v;
        return true;
    }
};

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr), cout.tie(nullptr);
    auto solve = []() {
        int n, m;
        cin >> n >> m;
        vector<int> nxt(n);
        vector<pair<int, int>> neq;
        DSU dsu(n);
        for (int i = 1; i < n; i++) {
            cin >> nxt[i];
            if (nxt[i] > nxt[i - 1] + 1) {
                return 0;
            }
            for (int j = nxt[i - 1]; j + 1 > nxt[i] && j > 0; j = nxt[j - 1]) {
                neq.emplace_back(j, i);
            }
            if (nxt[i] > 0) {
                dsu.merge(nxt[i] - 1, i);
            } else {
                neq.emplace_back(0, i);
            }
        }
        for (auto [x, y] : neq) {
            if (dsu.getfa(x) == dsu.getfa(y)) {
                return 0;
            }
        }
        int ans = m;
        for (int i = 1; i < n; i++) {
            if (nxt[i] == 0) {
                set<int> p = {dsu.getfa(0)};
                for (int j = nxt[i - 1]; j > 0; j = nxt[j - 1]) {
                    p.insert(dsu.getfa(j));
                }
                if ((int)p.size() >= m) {
                    return 0;
                }
                ans = ans * ll(m - p.size()) % M;
            }
        }
        return (ans % M + M) % M;
    };
    cout << solve() << '\n';
    return 0;
}