Yuki has two integers $l$ and $r$. She wants you to solve a massive Diophantine equation, but it is simply too massive! Therefore, Yuki decides to test you instead: how many positive integers $x$ cannot be represented as a sum of one or more positive integers in the range $[l, r]$? Specifically, if there are infinitely many such integers, output infty.

Input

The input contains multiple test cases.

The first line contains an integer $t$ ($1 \leq t \leq 10^5$), representing the number of test cases. For each test case:

• A single line containing two integers $l, r$ ($1 \leq l \leq r \leq 10^9$).

Output

For each test case: if the answer is finite, output a single integer on a line; otherwise, output the string infty.

Examples

Input 1

3
3 4
1 5
7 7

Output 1

3
0
infty

Note

For the first test case, only $x = 1, 2, 5$ cannot be represented.

For the third test case, it is clear that any $x$ such that $7 \nmid x$ cannot be represented.