Polyhedron

Time limit5sMemory limit256 MB

Summary

For each test case, compute the face count of a convex polyhedron from V and E with Euler formula F = 2 - V + E.

Level: Easy1 of 10
Topics: Math
Solved: No attempts yet

Problem

A mathematician carved a sphere into a convex polyhedron. Writing $V$ for the number of vertices, $E$ for the number of edges and $F$ for the number of faces, he knows that every convex polyhedron satisfies $V - E + F = 2$ . Carving spheres is his hobby, so when he writes down a record he counts only the vertices and the edges and never the faces.

Given the recorded $V$ and $E$ , find the number of faces of the convex polyhedron.

Input

The first line contains a natural number $T$ . ( $1 \le T \le 100$ )

Each of the next $T$ lines contains two natural numbers $V$ and $E$ separated by a space. ( $4 \le V \le 100$ , $4 \le E \le 100$ ) $V$ is the number of vertices and $E$ is the number of edges.

Output

For each $V$ and $E$ , print the number of faces of the convex polyhedron on its own line.

Examples3

Example 1
Input
```
2
8 12
4 6
```
Expected output
```
6
4
```
Example 2
Input
```
1
4 6
```
Expected output
```
4
```

Example 3

Input

Expected output