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++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <bits/stdc++.h>

#ifdef NON_SUBMIT
#define TEST(n) (n)
#else
#define TEST(n) ((void)0)
#endif

using namespace std;

int main()
{
	ios_base::sync_with_stdio(false);
	cin.tie(NULL); cout.tie(NULL);
	TEST(freopen("input.txt", "r", stdin));
	TEST(freopen("output.txt", "w", stdout));
	TEST(freopen("debug.txt", "w", stderr));
	int T, A, B, rtV, ans;
	long long V;
	for (cin >> T; T; T--) {
		cin >> A >> B;
		V = 1LL * A*B - 1;
		ans = 2 * (rtV = int(sqrt(V) + 1e-9));
		if (rtV == V / rtV) ans--;
		if (A <= rtV || V / A && V / (V / A) == A) ans--;
		if (B <= rtV || V / B && V / (V / B) == B) ans--;
		cout << ans << '\n';
	}
	return 0;
}