A range [L..H] is called a K-Frequent Prime range if there are at least K primes amongst the numbers L, L+1, ... H. Given N and K, calculate how many subranges of the range [2..N] are K-Frequent Prime.

Input

The first line contains the number of test cases T. Each of the next T lines contains 2 integers N and K.

Output

Output T lines, one corresponding to each test case, containing the required answer.

Constraints

1 <= T <= 100

2 <= N <= 100000

0 <= K <= 10000

Example

Input:
4
2 1
5 2
5 1
9 3

Output:
1
4
9
8

Explanation

Note: For the first test case, the only valid subrange is [2..2], whereas for the second test case, the valid subranges are: [2..3], [2..4], [2..5], [3..5].