#include <bits/stdc++.h>
// #include <ext/pb_ds/assoc_container.hpp>
// #include <ext/pb_ds/tree_policy.hpp>
#define SS ios_base::sync_with_stdio(0);cin.tie(nullptr);cout.tie(nullptr);
#pragma optimize("g", on)
#pragma GCC optimize("03")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,avx2,mmx,fma,avx,tune=native")
#define int long long
#define all(x) x.begin(),x.end()
#define F first
#define S second
using namespace std;
// using namespace __gnu_pbds;
// #define ordered_set tree<int,null_type,less_equal<int>,rb_tree_tag,tree_order_statistics_node_update>
const int LG = 20,N = 2e5+1,inf = 1e9,MOD = 998244353;
const double eps = 1e-9;
int T;
void solve() {
int n,m;
cin>>n>>m;
int a[n+1],b[n+1];
for(int i=1;i<=n;i++){
cin>>a[i];
}
for(int i=1;i<=n;i++){
cin>>b[i];
a[i]=max(a[i],b[i]);
}
auto ch = [&](int x){
int d=0;
for(int i=1;i<=n;i++){
if(a[i]*m>=x){
d+=(x+a[i]-1)/a[i];
}
else{
d+=m+(x-a[i]*m+b[i]-1)/b[i];
}
if(d>n*m) return 0;
}
return 1;
};
int l=1,r=1e18;
int res=0;
while(l<=r){
int mid=(l+r)/2;
if(ch(mid)){
res=mid;
l=mid+1;
}
else{
r=mid-1;
}
}
cout<<res;
return;
}
signed main() {
// freopen("deleg.in","r",stdin);
// freopen("deleg.out","w",stdout);
SS
int t = 1;
if (T) {
cin >> t;
}
while (t--) {
solve();
}
}
/*
*/
