Problem:
Score : 700 points

Problem Statement

10^{10^{10}} participants, including Takahashi, competed in two programming contests.
In each contest, all participants had distinct ranks from first through 10^{10^{10}}-th.

The score of a participant is the product of his/her ranks in the two contests.

Process the following Q queries:

In the i-th query, you are given two positive integers A_i and B_i. Assuming that Takahashi was ranked A_i-th in the first contest and B_i-th in the second contest, find the maximum possible number of participants whose scores are smaller than Takahashi's.

Constraints

1 \leq Q \leq 100

1\leq A_i,B_i\leq 10^9(1\leq i\leq Q)

All values in input are integers.

Input

Input is given from Standard Input in the following format:

Q
A_1 B_1
:
A_Q B_Q

Output

For each query, print the maximum possible number of participants whose scores are smaller than Takahashi's.

Sample Input 1

8
1 4
10 5
3 3
4 11
8 9
22 40
8 36
314159265 358979323

Sample Output 1

1
12
4
11
14
57
31
671644785

Let us denote a participant who was ranked x-th in the first contest and y-th in the second contest as (x,y).

In the first query, (2,1) is a possible candidate of a participant whose score is smaller than Takahashi's. There are never two or more participants whose scores are smaller than Takahashi's, so we should print 1.

Solution in C (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <stdio.h>

#define Rep(i,n) for(int (i)=0;(i)<(n);(i)++)
#define Min(a,b) ((a)<(b)?(a):(b))

typedef long long ll;

ll solve(ll a,ll b){
	ll cnt=0,lim=a*b-1;
	for(ll i=1;i<a*b;i++){
		if(i==a) continue;
		ll now=a*b/i;
		while(now*i==a*b||now==b) now--;
		if(0<now) cnt++;
		lim=Min(lim,now)-1;
		if(lim==b) lim--;
		if(lim<=0) break;
	}
	return cnt;
}

int main(){ 
	int q;
	scanf("%d",&q);
	Rep(i,q){
		ll a,b;
		scanf("%lld %lld",&a,&b);
		printf("%lld\n",solve(a,b));
	}
	return 0;
}