#include<iostream>
#include<cstdio>
#include<cmath>
#include<string>
#include<queue>
#include<algorithm>
#include<stack>
#include<cstring>
#include<vector>
#include<list>
#include<set>
#include<map>
using namespace std;
#define ll long long
#define mod 1000000007
#define inf 999999999
//#pragma comment(linker, "/STACK:102400000,102400000")
int scan()
{
    int res = 0 , ch ;
    while( !( ( ch = getchar() ) >= ‘0‘ && ch <= ‘9‘ ) )
    {
        if( ch == EOF ) return 1 << 30 ;
    }
    res = ch - ‘0‘ ;
    while( ( ch = getchar() ) >= ‘0‘ && ch <= ‘9‘ )
        res = res * 10 + ( ch - ‘0‘ ) ;
    return res ;
}
int a[100010];
int b[100010];
int gcd(int x,int y)
{
    if(x%y==0)
    return y;
    else
    return gcd(y,x%y);
}
void exgcd(int a, int b, int &x, int &y)
{
    if(b == 0)
    {
        x = 1;
        y = 0;
        return;
    }
    exgcd(b, a % b, x, y);
    int tmp = x;
    x = y;
    y = tmp - (a / b) * y;
}
int main()
{
    int x,y,z,i,t;
    scanf("%d",&x);
    while(x--)
    {
        scanf("%d%d",&y,&z);
        for(i=0;i<z;i++)
        scanf("%d",&b[i]);
        for(i=0;i<z;i++)
        scanf("%d",&a[i]);
        int a1=a[0],b1=b[0];
        int jie=1;
        for(i=1;i<z;i++)
        {
            int a2=a[i],b2=b[i];
            int xx,yy;
            int gys=gcd(b1,b2);
            if((a2-a1)%gys)
            {
                jie=0;
                break;
            }
            exgcd(b1,b2,xx,yy);
            xx=(xx*(a2-a1))/gys;
            int gbs=b1*b2/gys;
            a1=(((xx*b1+a1)%gbs)+gbs)%gbs;
            b1=gbs;
        }
        if(!jie||y<a1)
        printf("0\n");
        else
        printf("%d\n",(y-a1)/b1+1-((a1==0)?1:0));
    }
    return 0;
}