#include<bits/stdc++.h>
#define rep(i,a,b) for(int i=a;i<=(b);++i)
#define per(i,a,b) for(int i=a;i>=(b);--i)
#define in(x) scanf("%d",&x)
#define ind(x) scanf("%lld",&x)
#define out(x) printf("%d ",x);
#define outln(x) printf("%lld\n",x);
#define bug(x) cout<<#x<<" is "<<x<<endl
#define mem(a,x) memset(a,x,sizeof(a))
#define pb push_back
using namespace std;
typedef long long ll;
const ll mod=1e9+7;
#define PE(x,y) x=((x)+(y))%mod
ll gcd(ll a,ll b) { return b?gcd(b,a%b):a;}
ll powmod(ll a,ll b) {ll res=1;a%=mod;
for(;b;b>>=1){if(b&1)res=res*a%mod;a=a*a%mod;}return res;}
const int N=1e5+10;
int main()
{
//freopen("input.txt", "r", stdin);
}#include<bits/stdc++.h>
#define rep(i,a,b) for(in