#include<stdio.h>
#include<algorithm>
#include<string.h>
#include<stdlib.h>

using namespace std;

const int M = 20;
typedef long long ll;
int r;
ll n[M], b[M], N;

void gcd(ll a, ll b, ll &x, ll &y)
{
    if(b == 0)
    {
        x = 1;
        y = 0;
        r = a;
        return ;
    }
    gcd(b, a % b, x, y);
    ll t = x;
    x = y;
    y = t - a / b * y;
}
ll CRT2(ll b[], ll n[], int m)
{
    int f = 0;
    ll n1 = n[0], n2, b1 = b[0], b2, c, t, k, x, y;
    for(int i = 1 ; i < m ; i++)
    {
        n2 = n[i];
        b2 = b[i];
        c = b2 - b1;
        gcd(n1, n2, x, y);
        if(c % r != 0)
        {
            f = 1;
            break;
        }
        k = c / r * x;
        t = n2 / r;
        k = (k % t + t) % t;
        b1 = b1 + n1 * k;
        n1 = n1 * t;
    }
    if(f)//无解
        return 0;
    if(b1 == 0)
        b1 = n1;
    if(b1 > N)
        return 0;
    return (N - b1) / n1 + 1;
}

int main()
{
    int t, m;
    scanf("%d", &t);
    while(t--)
    {
        scanf("%lld%d", &N, &m);
        for(int i = 0 ; i < m ; i++)
            scanf("%lld", &n[i]);
        for(int i = 0 ; i < m ; i++)
            scanf("%lld", &b[i]);
        printf("%lld\n", CRT2(b, n, m));
    }
    return 0;
}