#include <bits/stdc++.h>
using namespace std;
long long a[100005], f[100005], j, k, m, d, x, y, n, ans, R, L;
vector<int> v[100005];
long long go(int u) {
  f[u] = 1;
  if (a[u] > L || a[u] < R) return 1;
  if (a[u] == L && u < j) return 1;
  long long res = 1;
  for (int i = 0; i < v[u].size(); i++) {
    if (f[v[u][i]]) continue;
    res = (res * (go(v[u][i]))) % (int(1e9 + 7));
  }
  return res + 1;
}
int main() {
  cin >> d >> n;
  for (j = 1; j <= n; j++) cin >> a[j];
  for (j = 1; j < n; j++) {
    cin >> x >> y;
    v[x].push_back(y);
    v[y].push_back(x);
  }
  for (j = 1; j <= n; j++) {
    L = a[j];
    R = a[j] - d;
    ans = (ans + go(j) - 1) % (int(1e9 + 7));
    for (int e = 1; e <= n; e++) f[e] = 0;
  }
  cout << ans << endl;
  cin >> m;
}

### Prompt

Your task is to create a Cpp solution to the following problem:

As you know, an undirected connected graph with n nodes and n - 1 edges is called a tree. You are given an integer d and a tree consisting of n nodes. Each node i has a value ai associated with it.

We call a set S of tree nodes valid if following conditions are satisfied:

  1. S is non-empty.
  2. S is connected. In other words, if nodes u and v are in S, then all nodes lying on the simple path between u and v should also be presented in S.
  3. <image>.



Your task is to count the number of valid sets. Since the result can be very large, you must print its remainder modulo 1000000007 (109 + 7).

Input

The first line contains two space-separated integers d (0 ≤ d ≤ 2000) and n (1 ≤ n ≤ 2000).

The second line contains n space-separated positive integers a1, a2, ..., an(1 ≤ ai ≤ 2000).

Then the next n - 1 line each contain pair of integers u and v (1 ≤ u, v ≤ n) denoting that there is an edge between u and v. It is guaranteed that these edges form a tree.

Output

Print the number of valid sets modulo 1000000007.

Examples

Input

1 4
2 1 3 2
1 2
1 3
3 4


Output

8


Input

0 3
1 2 3
1 2
2 3


Output

3


Input

4 8
7 8 7 5 4 6 4 10
1 6
1 2
5 8
1 3
3 5
6 7
3 4


Output

41

Note

In the first sample, there are exactly 8 valid sets: {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {3, 4} and {1, 3, 4}. Set {1, 2, 3, 4} is not valid, because the third condition isn't satisfied. Set {1, 4} satisfies the third condition, but conflicts with the second condition.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
long long a[100005], f[100005], j, k, m, d, x, y, n, ans, R, L;
vector<int> v[100005];
long long go(int u) {
  f[u] = 1;
  if (a[u] > L || a[u] < R) return 1;
  if (a[u] == L && u < j) return 1;
  long long res = 1;
  for (int i = 0; i < v[u].size(); i++) {
    if (f[v[u][i]]) continue;
    res = (res * (go(v[u][i]))) % (int(1e9 + 7));
  }
  return res + 1;
}
int main() {
  cin >> d >> n;
  for (j = 1; j <= n; j++) cin >> a[j];
  for (j = 1; j < n; j++) {
    cin >> x >> y;
    v[x].push_back(y);
    v[y].push_back(x);
  }
  for (j = 1; j <= n; j++) {
    L = a[j];
    R = a[j] - d;
    ans = (ans + go(j) - 1) % (int(1e9 + 7));
    for (int e = 1; e <= n; e++) f[e] = 0;
  }
  cout << ans << endl;
  cin >> m;
}

```