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There is a large tree house in an unknown world. It is ruled by the great emperor KZS. It consists of N nodes numbered from 1 to N in which the people of that world reside. The nodes are organized in a tree structure rooted at node 1. You need to assign values to the nodes according to the wishes of emperor KZS which are as follows :-

  • The value of node 1 is X.
  • All immediate children of any node have pairwise distinct values.
  • For every node with at least one immediate child, the gcd of the values of all immediate children is equal to the value of the node.
  • The total sum of the values of all nodes should be minimum.

The greatest common divisor gcd(a,b) of two positive integers a and b is equal to the largest integer d such that both integers a and b are divisible by d.

Print the sum of all values, modulo 109+7.

Input

  • The first line contains an integer T, the number of test cases. T testcases follow.
  • The first line of each test contains two integers N and X.
  • Each of the following N−1 lines contains two integers u and v, denoting an edge between nodes u and v.

Output

  • For each test case, print the sum of values, modulo 109+7.

Constraints

  • 1≤T≤15
  • 2≤N≤3⋅105
  • 1≤X≤109
  • 1≤u,v≤N and u≠v
  • The given edges form a tree
  • The sum of N over all test cases doesn't exceed 3⋅105.

Subtasks

Subtask #1 (100 points): Original Constraints

Sample Input

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

Sample Output

7
11

Explanation

In test case 1, we will give values 1, 2, 3 to the nodes 2, 3 and 4 respectively. So, the total sum will be 1+1+2+3=7.

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