Reach The Point

Start from (0,0) with initial strength K=1. One operation either increases x by K, increases y by K, or increases K by 1. Find the minimum number of operations to reach exactly (a,b); each test case is independent.

输入格式

The first line contains t, followed by t lines of a b. Full original bounds: 1≤t≤1000, 1≤a,b≤10^9.

输出格式

For each test case, output one line with the minimum number of operations, t lines in total.

样例 1

输入：

1
1 6

输出：

5

样例 2

输入：

1
1 1

输出：

2

样例 3

输入：

2
2 3
6 6

输出：

4
6

样例说明

The outputs of the three public examples are, in order: 5; 2; 4 / 6. They have been checked by independent enumeration or direct simulation.