Problem E: Sequence

Time Limit: 1 Second Memory Limit: 65536 KB

We inductively label the nodes of a rooted binary tree with an infinite number of nodes as follows:

The root is labeled by 1/1,
If the label of a node is p/q, then
- The label of its left child is p/(p+q), and
- The label of its right child is (p+q)/q.

By having this tree in our hand, we define a rational sequence a₁, a₂, a₃, … by a breadth first traversal of the tree in such a way that nodes in the same level are visited from left to right. Therefore, we have a₁=1/1, a₂=1/2, a₃=2/1, a₄=1/3, a₅=3/2, …

You are to write a program that gets values p and q and computes an integer n for which a_n=p/q.

Input

The first line of the input includes the number of test cases, 1≤t≤1000. Each test case consists of one line. This line contains p, followed by / and then q without any space between them.

Output

For each test case, output in one line an integer n for which a_n=p/q. It is guaranteed that in all test cases n fits in a 32-bit integer.

Sample Input

4
1/1
1/3
5/2
2178309/1346269

Sample Output

Submit