#include <bits/stdc++.h>
using namespace std;

const int N = 3e4 + 5;
const int mod = 1e9 + 7;

int tc;
int n, m, K;
int fa[N];

inline int lca(int u, int v) {
  map<int, int> mp;
  int cur = u;
  while (cur) {
    mp[cur] = 1;
    cur = fa[cur];
  }
  cur = v;
  while (mp.find(cur) == mp.end()) {
    cur = fa[cur];
  }
  return cur;
}

namespace Sub1 {
int bl[N];
inline int find(int u) {
  while (u != bl[u]) {
    u = bl[u] = bl[bl[u]];
  }
  return u;
}
inline void merge(int u, int v) {
  u = find(u), v = find(v);
  bl[u] = v;
}

int to[N];
inline int LCA(int u, int v) {
  map<int, int> mp;
  int cur = u;
  while (cur) {
    mp[cur] = 1;
    cur = to[cur];
  }
  cur = v;
  while (mp.find(cur) == mp.end()) {
    cur = to[cur];
  }
  return cur;
}

int ans;
void check() {
  int tot = n + m;
  if (count(to + 1, to + tot + 1, 0) != 1) return;
  iota(bl + 1, bl + tot + 1, 1);
  for (int i = 1; i <= tot; i++) if (to[i]) {
    merge(to[i], i);
  }
  int cnt = 0;
  for (int i = 1; i <= tot; i++) cnt += (bl[i] == i);
  if (cnt > 1) return;
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
      if (lca(i, j) != LCA(i, j)) return;
    }
  }
  for (int i = 1; i <= tot; i++) {
    for (int j = 1; j <= tot; j++) {
      int u = LCA(i, j);
      if (u > max(i, j) + K) return;
    }
  }
  (++ans) %= mod;
}
void dfs(int u) {
  if (u == n + m + 1) {
    check();
    return;
  }
  for (int v = 0; v <= n + m; v++) {
    if (u == v) continue;
    to[u] = v;
    dfs(u + 1);
  }
}
void main() {
  dfs(1);
  cout << ans << "\n";
}
}

void solve() {
  cin >> n >> m >> K;
  for (int i = 2; i <= n; i++) {
    cin >> fa[i];
  }
  if (m == 0) {
    cout << 1 << "\n";
    return;
  }
  if (m == 1) {
    cout << (2 * n - 1) % mod << "\n";
    return;
  }
  if (m == 2) {
    int ans = 0;
    if (K > 0) {
      (ans += n * 2 % mod) %= mod;
      (ans += 1ll * n * n % mod) %= mod;
      (ans += 1ll * (n - 1) * n * 2 % mod) %= mod;
      (ans += 1ll * (n - 1) * (n - 2) % mod) %= mod;
      (ans += 4ll * (n - 1) % mod) %= mod;
    } else {
      (ans += n * 2 % mod) %= mod;
      (ans += 1ll * n * n % mod) %= mod;
      (ans += 1ll * (n - 1) * n * 2 % mod) %= mod;
      (ans += 1ll * (n - 1) * (n - 2) % mod) %= mod;
      (ans += 3ll * (n - 1) % mod) %= mod;
    }
    cout << ans << "\n";
    return;
  }
  if (n + m <= 8) {
    Sub1::main();
  }
}

int main() {
  cin.tie(0)->sync_with_stdio(0);
  int t;
  cin >> tc >> t;
  while (t--) solve();
  return 0;
}