GCD2

Problem Statement

Frank explained its friend Felman the algorithm of Euclides to calculate the GCD of two numbers. Then Felman implements it algorithm

int gcd(int a, int b)
{
 if (b==0)
  return a;
 else
  return gcd(b,a%b);
}

and it proposes to Frank that makes it but with a little integer and another integer that has up to 250 digits.

Your task is to help Frank programming an efficient code for the challenge of Felman.

Input

The first line of the input file contains a number representing the number of lines to follow. Each line consists of two number A and B (0 <= A <= 40000 and A <= B < 10^250).

Output

Print for each pair (A,B) in the input one integer representing the GCD of A and B.

Example

Input:
2
2 6
10 11


Output:
2
1

Problem Link : GCD2

The idea:  

• gcd(b,a)=gcd(a,a%b);
• Now one has to  use the concept of modulo arithmetic. Accept the value of b as string.
• Extract each digit as dig=b[i]-'0'.
• Now use rem=((dig*10)%a+b%a)%a;
• now use ans=gcd(a,rem)

The Code:

#include<iostream>

#include<bits/stdc++.h>

using namespace std;

int gcd(int a,int b)

{

    if(b==0)

    return a;

    else

    {

        int ans=gcd(b,a%b);

        return ans;

    }

}

int main()

{

    int T;

    scanf("%d",&T);

    while(T--)

    {

        int a;

        string b;

        cin>>a;

        cin>>b;

        if(a==0)

        {

            cout<<b<<endl;

            continue;

        }

        else

        {

        int rem=0;

        for(int i=0;i<b.length();i++)

        {

            int dig=b[i]-'0';

            rem=((rem*10)%a+dig%a)%a;

        }

        cout<<gcd(a,rem)<<endl;

        }

    }

    

}