Given a tree with n nodes, each node has a value of 1 or −1. For q queries (u,v), count the number of nodes t on the simple path from u to v such that the sum of node values on the simple path from u to t is positive.
### Input
- The first line contains two integers n and q.
- The second line contains n integers representing the values of the nodes from 1 to n.
- The next n−1 lines each contain two integers u,v representing an edge of the tree.
- The next q lines each contain two integers u,v representing a query.
### Output
- For each query, print a single integer as the answer.
### Constraints
- 1≤n,q≤105.
- 1≤u,v≤n.
### Example
Input:
85−1111−111−1155636454748123822172764
Output:
51022