Codeforces Round #277 (Div. 2)D（树形DP计数类）_html/css_WEB-ITnose

D. Valid Sets

time limit per test

memory limit per test

input

output

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. .

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).

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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.

Sample test(s)

input

1 42 1 3 21 21 33 4

output

input

0 31 2 31 22 3

output

input

4 87 8 7 5 4 6 4 101 61 25 81 33 56 73 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.

题意：RT

思路：树形DP，dp[u]表示以u为根，且它的所有子树的点v的权值都不超过它，且满足 w[u]-w[v]

            对于每个点为根这样算一遍就好了，注意减去算重的情况，即相邻多个点的权值相等，可以用点的代号去重（即规定只能从代号大的往小的DP）