4576: Digit Tree
内存限制：256 MB
时间限制：2 S
题面：传统
评测方式：文本比较
上传者：
提交：1
通过：1
题目描述
time limit per test
3 secondsmemory limit per test
256 megabytesinput
standard inputoutput
standard outputZS the Coder has a large tree. It can be represented as an undirected connected graph of n vertices numbered from 0 to n-1 and n-1 edges between them. There is a single nonzero digit written on each edge.
One day, ZS the Coder was bored and decided to investigate some properties of the tree. He chose a positive integer M, which is coprime to 10, i.e.
.
ZS consider an ordered pair of distinct vertices (u,v) interesting when if he would follow the shortest path from vertex u to vertex v and write down all the digits he encounters on his path in the same order, he will get a decimal representaion of an integer divisible by M.
Formally, ZS consider an ordered pair of distinct vertices (u,v) interesting if the following states true:
One day, ZS the Coder was bored and decided to investigate some properties of the tree. He chose a positive integer M, which is coprime to 10, i.e.
.ZS consider an ordered pair of distinct vertices (u,v) interesting when if he would follow the shortest path from vertex u to vertex v and write down all the digits he encounters on his path in the same order, he will get a decimal representaion of an integer divisible by M.
Formally, ZS consider an ordered pair of distinct vertices (u,v) interesting if the following states true:
- Let a1=u,a2,...,ak=v be the sequence of vertices on the shortest path from u to v in the order of encountering them;
- Let di (1≤i<k) be the digit written on the edge between vertices ai and ai+1;
- The integer
is divisible by M.
Input
The first line of the input contains two integers, n and M (2≤n≤100000,1≤M≤109, 
)− the number of vertices and the number ZS has chosen respectively.The next n-1 lines contain three integers each. i-th of them contains ui,vi and wi, denoting an edge between vertices ui and vi with digit wi written on it (0≤ui,vi<n,1≤wi≤9).
Output
Print a single integer− the number of interesting (by ZS the Coder's consideration) pairs.Examples
Input
6 7
0 1 2
4 2 4
2 0 1
3 0 9
2 5 7
Output
7
Input
5 11
1 2 3
2 0 3
3 0 3
4 3 3
Output
8
Note
In the first sample case, the interesting pairs are (0,4),(1,2),(1,5),(3,2),(2,5),(5,2),(3,5). The numbers that are formed by these pairs are 14,21,217,91,7,7,917 respectively, which are all multiples of 7. Note that (2,5) and (5,2) are considered different. 
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输出样例 复制