#include<iostream>
#include<functional>
#include<vector>
#include<set>
#include<queue>
#include<map>
#include<algorithm>
#include<numeric>
#include<cmath>
#include<cstring>
#include<bitset>
#include<iomanip>
#include<random>
#include<fstream>
#include<complex>
#include<time.h>
#include<stack>
#include<cassert>
using namespace std;
#define endl "\n"
#define ll long long
#define ch char
#define vec vector 
#define vll vector<ll> 
#define sll set<ll> 
#define pll pair<ll,ll> 
#define mkp make_pair
#define mll map<ll,ll> 
#define puf push_front
#define pub push_back
#define pof pop_front()
#define pob pop_back()
#define em empty()
#define fi first
#define se second
#define fr front()
#define ba back()
#define be begin()
#define rbe rbegin()
#define en end()
#define ren rend()
#define all(x) x.begin(),x.end()
#define rall(x) x.rbegin(),x.rend()
#define fo(i,x,y) for(ll i=x;i<=y;++i)
#define fa(i,v) for(auto &i:v)
#define re return 
#define sz size()
#define so(v) sort(all(v))
#define pop_count(x) __builtin_popcount(x)
#define rso(v) sort(rall(v))
#define rev(v) reverse(all(v))
#define i(x) for(ll i=0;i<x;++i)
#define j(x) for(ll j=0;j<x;++j)
#define k(x) for(ll k=0;k<x;++k)
#define xx(k) while(k--)

#define wh(x) while(x)
#define st string
//10^x      8765432109876543210
#define MAX 8611686018427387000
#define zeros(x) __builtin_ctzll(x)
#define in insert
#define uniq(v) v.erase(unique(all(v)),v.en);
#define er(i,n) erase(i,n);
//#define co(x,a) count(all(x),a)
#define lo(v,a) lower_bound(v.begin(),v.end(),a)
#define up(v,a) upper_bound(v.begin(),v.end(),a)
#define dou double
#define ge(x,...) x __VA_ARGS__; ci(__VA_ARGS__);
#define fix(n,ans) cout<<fixed<<std::setprecision(n)<<ans<<endl;


void cc(){ cout<<endl; };
void ff(){ cout<<endl; };
void cl(){ cout<<endl; };
template<class T,class... A> void ff(T a,A... b){ cout<<a; (cout<<...<<(cout<<' ',b)); cout<<endl; }; 
template<class T,class... A> void cc(T a,A... b){ cout<<a; (cout<<...<<(cout<<' ',b)); cout<<' '; }; 
template<class T,class... A> void cl(T a,A... b){ cout<<a; (cout<<...<<(cout<<'\n',b)); cout<<endl; }; 
template<class T,class... A> void cn(T a,A... b){ cout<<a; (cout<<...<<(cout<<"",b));  }; 
template<class... A> void ci(A&... a){ (cin>>...>>a); }; 
template<class T>void ou(T v){fa(i,v)cout<<i<<" ";cout<<endl;} 
template<class T>void oun(T v){fa(i,v)cout<<i;cout<<endl;} 
template<class T>void ouu(T v){fa(i,v){fa(j,i)cout<<j<<" ";cout<<endl;}} 
template<class T> void oul(T v){fa(i,v)cout<<i<<endl;} 
template<class T>void in(T &v){fa(i,v)cin>>i;}
template<class T>void inn(T &v){fa(i,v)fa(j,i)cin>>j;}
template<class T>void oump(T &v){fa(i,v)ff(i.fi,i.se);}

template<class T,class A>void pi(pair<T,A> &p){ci(p.fi,p.se);}
template<class T,class A>void po(pair<T,A> &p){ff(p.fi,p.se);}
template<class T,class... A> void fl(T a,A... b){ cout<<a; (cout<<...<<(cout<<' ',b)); cout<<endl<<flush; }; 

ll mod = 1000000007;
ll mod9= 998244353;
void init();
void solve();
/*
void ori();
ll random_(){
		  std::random_device seed_gen;
		  std::mt19937 engine(seed_gen());
		  // [-1.0, 1.0)の値の範囲で、等確率に実数を生成する
		  std::uniform_real_distribution<> dist1(1.0, 100000);
		  i(10000){ // 各分布法に基いて乱数を生成
					 ll n  = dist1(engine);
		  } return 0;
}
*/
mll to_prime(ll x){
		  mll mp;
		  for(ll i=2;i*i<=x;++i){
					 while(x%i==0){
								++mp[i];
								x/=i;
					 }
		  }
		  if(x!=1)
					 ++mp[x];
		  re mp;
}
#define acc(v) accumulate(v.begin(),v.end(),0LL)
#define acci(v,i) accumulate(v.begin(),v.begin()+i,0LL)
#define dll deque<ll>
int main(void){
		  init();
		  solve();
		  return 0;
}
template <typename T>class pnt{
		  public:
					 T x,y;
					 pnt(T x=0,T y=0):x(x),y(y){}
					 pnt operator + (const pnt r)const {
								return  pnt(x+r.x,y+r.y);}
					 pnt operator - (const pnt r)const {
								return  pnt(x-r.x,y-r.y);}
					 pnt operator * (const pnt r)const {
								return  pnt(x*r.x,y*r.y);}
					 pnt operator / (const pnt r)const {
								return  pnt(x/r.x,y/r.y);}
					 pnt &operator += (const pnt r){
								x+=r.x;y+=r.y;return *this;}
					 pnt &operator -= (const pnt r){
								x-=r.x;y-=r.y;return *this;}
					 pnt &operator *= (const pnt r){
								x*=r.x;y*=r.y;return *this;}
					 pnt &operator /= (const pnt r){
								x/=r.x;y/=r.y;return *this;}
					 ll dist(const pnt r){
								re (x-r.x)*(x-r.x)+(y-r.y)*(y-r.y);
					 }
					 ll man(const pnt r){
								re abs(x-r.x)+abs(y-r.y);
					 }
					 pnt rot(const dou theta){
								T xx,yy;
								xx=cos(theta)*x-sin(theta)*y;
								yy=sin(theta)*x+cos(theta)*y;
								return pnt(xx,yy);
					 }
};
istream &operator >> (istream &is,pnt<dou> &r){is>>r.x>>r.y;return is;}
ostream &operator << (ostream &os,pnt<dou> &r){os<<r.x<<" "<<r.y;return os;}

struct BIT{
	ll n;vll v;
	BIT(ll n):n(n+n%2),v(2*(n+n%2)){};
	ll op(ll x,ll y){
		re gcd(x,y);
	}
	ll sum(ll i){
		ll s=0;
		while(i){
			s=gcd(s,v[i]);
			i-=i&-i;
		}
		re s;
	}
	void add(ll i,ll x){
		while(i<=n){
			v[i]=op(v[i],x);
			i+=i&-i;
		}
	}
	ll ran(ll l,ll r){
		re op(sum(--l),sum(r));
	}
};
template<class T>bool chmaxeq(T& a, const T& b) { if (a <= b) { a = b; return 1; } return 0; }
template<class T>bool chmineq(T& a, const T& b) { if (b <= a) { a = b; return 1; } return 0; }
template<class T>bool chmax(T& a, const T& b) { if (a < b) { a = b; return 1; } return 0; }
template<class T>bool chmin(T& a, const T& b) { if (b < a) { a = b; return 1; } return 0; }

struct Trie{
	struct Node{
		vll nxt;
		vec<st> done;
		ll dep,cnt=0;
		Node(ll c_):nxt(30),dep(c_){}
	};
	ll root=0;
	vec<Node>tree={Node(root)};
	void ins(st s){
		ll c=0; 
		for(ll i=0;i<s.sz;++i){
			ll to=tree[c].nxt[s[i]-'a'];
			if(to==0){
				to=tree.sz;
				tree[c].nxt[s[i]-'a']=to;
				tree.pub(Node(i+1));
			}
			++tree[to].cnt;
			c=to;
		}
		tree[c].done.pub(s);
	}
	ll cal(st s){
		ll ans=0,c=0;
		for(ll i=0;i<s.sz;++i){
			ll to=tree[c].nxt[s[i]-'a'];
			if(tree[to].cnt>1)++ans;
			else break;
			c=to;
		}
		re ans;
	}
};
#define fo(i,x,y) for(ll i=x;i<=y;++i)
#define rfo(_ii,_xx,_yy) for(ll _ii=_xx;_ii>=_yy;--_ii)
#define qll queue<ll>

template<typename T> using pq= priority_queue<T>;
template<typename T> using pqg= priority_queue<T,vec<T>,greater<T>>;
vec<pair<ch,ll>>rle(st s){//run_length_encoding
	ll n=s.sz;
	vec<pair<ch,ll>>ans;
	for(ll i=0;i<n;++i){
		ll cnt=1;
		wh(i+1<n&&s[i+1]==s[i]){
			++cnt;++i;
		}
		ans.pub(mkp(s[i],cnt));
	}
	re ans;
}

vector<vector<ll>> mat_mul(vector<vector<ll>> a, vector<vector<ll>> b, ll mod) {
	// 行列乗算
	int n = a.size();
	vector<vector<ll>> res(n, vector<ll>(n));
	for (int i = 0; i < n; i++) {
		for (int j = 0; j < n; j++) {
			for (int k = 0; k < n; k++) {
				res[i][j] += a[i][k] * b[k][j];
				res[i][j] %= mod;
			}
		}
	}
	return res;
}

vector<vector<ll>> mat_pow(vector<vector<ll>> a, ll b, ll mod) {
	// 行列累乗
	int n = a.size();
	vector<vector<ll>> res(n, vector<ll>(n));
	for (int i = 0; i < n; i++) res[i][i] = 1;
	while (b) {
		if (b & 1) res = mat_mul(res, a, mod);
		a = mat_mul(a, a, mod);
		b >>= 1;
	}
	return res;
}


void Yes(bool f){
		ff(f?"Yes":"No");re;
}
void yes(bool f){
		ff(f?"yes":"no");re;
}
void YES(bool f){
		ff(f?"YES":"NO");re;
}
void sub();
template <class T>
struct Edge {
    int rv, from, to;  // rev:逆向きの辺の番号
    T cap, original_cap;
    Edge(int f, int t, T c,int r ) : rv(r), from(f), to(t), cap(c), original_cap(c) {}
};

template <class T>
struct Graph {
    vector<vector<Edge<T>>> G;
    Graph(int n = 0) : G(n) {}

    vector<Edge<T>>& operator[](int i) { return G[i]; }//G[i]でi番目の辺を返す
    const size_t size() const { return G.size(); }//
    Edge<T>& redge(Edge<T> e) {  // 逆向きの辺を返す
        return G[e.to][e.rv];   // 自己ループはないと仮定（あれば G[e.to][e.rev + 1] とする必要がある）
    }
    void add_edg(int from, int to, T cap) {  // 有向辺を加える
        G[from].push_back( Edge<T>(  from, to, cap,(int)G[to].size() ));
        G[to].push_back(Edge<T>( to, from, 0 ,(int)G[from].size() - 1));
    }
};

/* FordFulkerson: Ford-Fulkersonのアルゴリズムで最大流を求める構造体
    max_flow(G,s,t)：sからtへのグラフGの最大流を求める
    副作用：G は最大流の残余ネットワークになる
    計算量: O(|f*||E|) (f*:最大流) (この最悪ケースになることはほぼ無い)
*/
template <class T>
struct Ford {
    const T INF = 1e9;
    vector<int> used;

    Ford(){};
    T dfs(Graph<T>& G, int v, int t, T f) {  // 増加可能経路を見つけて増加分のフローを返す
	    if (v == t) return f;
	    used[v] = true;
	    for (auto& e : G[v]) {
		    if (!used[e.to] && e.cap > 0) {
			    T d = dfs(G, e.to, t, min(f, e.cap));
			    if (d > 0) {
				    e.cap -= d;
				    G.redge(e).cap += d;
				    return d;
			    }
		    }
	    }
	    return 0;
    }
    T max_flow(Graph<T>& G, int s, int t) {
	    T flow = 0;
	    while (true) {
		    used.assign(G.size(), 0);
		    T f = dfs(G, s, t, INF);  // f が増加分のフロー
		    if (f == 0) {
			    return flow;
		    } else {
			    flow += f;
		    }
	    }
	    return 0;
    }
    /*
	  Ford<ll>f;
	  ff(f.max_flow(g,s,sink));
	  */
};
struct UF{ vll par,rk,siz; UF(ll n):par(n+5,-1),rk(n+5,0){ }
	ll root(ll x){ if(par[x]<0)return x; else return par[x]=root(par[x]); }
	bool same(ll x,ll y){ return root(x)==root(y); }
	bool unite(ll x,ll y){ 
		ll rx=root(x),ry=root(y); 
		if(rx==ry) return 0; 
		if(rk[rx]<rk[ry]) swap(rx,ry);
		par[rx]+=par[ry]; par[ry]=rx;
		if(rk[rx]==rk[ry]) rk[rx]++; return 1; 
	}
	ll size(ll x){ return -par[root(x)]; }
};
ll dijkstra(ll start,ll n){//O((n+m)log(n))
	vec<vec<pll>>e(n);
	vll dis(n+50,MAX);
	pqg<pll>q;q.push({0ll,start});
	dis[start]=0;
	while(q.em^1){
		auto [d,now]=q.top();q.pop();
		if(dis[now]<d)continue;
		if(now==n)re dis[now];
		for(auto[to,cst]:e[now])if(chmin(dis[to],cst+d)){
			q.push({dis[to],to});
		}
	}
	re -1;
}
struct UF_norank{ vll par,siz; UF_norank(ll n):par(n+5,-1){ }
	ll root(ll x){ if(par[x]<0)return x; else return par[x]=root(par[x]); }
	bool same(ll x,ll y){ return root(x)==root(y); }
	bool unite(ll from,ll to){ 
		ll r_fr=root(from),r_to=root(to); 
		if(r_fr==r_to) return 0; 
		par[r_to]+=par[r_fr]; par[r_fr]=r_to;
		return 1; 
	}
	ll size(ll x){ return -par[root(x)]; }
};
vll di(ll start,ll n,vec<vec<pll>>cost){//O((n+m)log(n))
	vll dis(n+5,MAX);
	pqg<pll>q;q.push({0ll,start});
	dis[start]=0;
	while(q.em^1){
		auto [d,now]=q.top();q.pop();
		if(dis[now]<d)continue;
		//if(now==goal)break;
		for(auto [to,cst]:cost[now]){
			if(chmin(dis[to],cst+d)){
				q.push({dis[to],to});
			}
		}
	}
	re dis;
}
vll z_algo(string pattern, string text) {//z algorithm 最長共通接頭辞
	string str = pattern + "$" + text;
	ll n = str.length(),np=pattern.sz;
	vll Z(n+5),ret(n+5);
	for (ll i = 1,L=0,R=0,j; i < n; ++i) {
		if (R<i) {
			L = R = i;
			while (R<n && str[R-L] == str[R])
				R++;
			Z[i] = R-L;
			if(i>np)
				ret[i-np-1]=Z[i];

			R--;
		}else{
			j= i-L;
			if (Z[j]<R-i+1){
				Z[i]=Z[j];
			}else{
				L = i;
				while (R<n && str[R-L] == str[R])
					R++;
				Z[i] = R-L;
				R--;
			}
			if(i>np)
				ret[i-np-1]=Z[i];
		}
	}
	//ff("z"); ou(Z);
	re ret;
}
// 2^10 = 1024
//vll dy={-1,-1,-1,0,0,1,1,1},dx={-1,0,1,-1,1,-1,0,1};
/* O(2*10^8) 9*10^18 1LL<<62 4*10^18
   ~~(v.be,v.be+n,x); not include v.be+n
   set.lower_bound(x);
   ->. *++~ ! /%* +- << < == & && +=?:
   */
//          12345678901234567890
//vll dy={-1,0,0,1},dx={0,-1,1,0};
const ll INF = mod * mod;
typedef pair<int, int>P;
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rp(i,n) for(int i=0;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
ll mod_pow(ll x, ll n, ll m = mod) {
	if (n < 0) {
		ll res = mod_pow(x, -n, m);
		return mod_pow(res, m - 2, m);
	}
	if (abs(x) >= m)x %= m;
	if (x < 0)x += m;
	//if (x == 0)return 0;
	ll res = 1;
	while (n) {
		if (n & 1)res = res * x % m;
		x = x * x % m; n >>= 1;
	}
	return res;
}
//mod should be <2^31
struct mint {
	int n;
	mint() :n(0) { ; }
	mint(ll m) {
		if (m < 0 || mod <= m) {
			m %= mod; if (m < 0)m += mod;
		}
		n = m;
	}
	operator int() { return n; }
};
bool operator==(mint a, mint b) { return a.n == b.n; }
bool operator<(mint a, mint b) { return a.n < b.n; }
mint operator+=(mint& a, mint b) { a.n += b.n; if (a.n >= mod)a.n -= (int)mod; return a; }
mint operator-=(mint& a, mint b) { a.n -= b.n; if (a.n < 0)a.n += (int)mod; return a; }
mint operator*=(mint& a, mint b) { a.n = ((ll)a.n * b.n) % mod; return a; }
mint operator+(mint a, mint b) { return a += b; }
mint operator-(mint a, mint b) { return a -= b; }
mint operator*(mint a, mint b) { return a *= b; }
mint operator^(mint a, ll n) {
	if (n == 0)return mint(1);
	mint res = (a * a) ^ (n / 2);
	if (n % 2)res = res * a;
	return res;
}
ll inv(ll a, ll p) {
	return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
mint operator/(mint a, mint b) { return a * mint(inv(b, mod)); }
mint operator/=(mint& a, mint b) { a = a / b; return a; }

bool operator==(mint a, ll b) {re a==mint(b);}
bool operator<(mint a, ll b) {re a<mint(b);}
mint operator+=(mint& a, ll b) {re a+=mint(b);}
mint operator-=(mint& a, ll b) {re a-=mint(b);}
mint operator*=(mint& a, ll b) {re a*=mint(b);}
mint operator+(mint a, ll b) {re a+mint(b);}
mint operator-(mint a, ll b) {re a-mint(b);}
mint operator*(mint a, ll b) {re a*mint(b);}
mint operator/(mint a, ll b) {re a/mint(b);}
mint operator/=(mint& a, ll b) {re a/=mint(b);}

bool operator==(ll a, mint b) {re mint(a)==b;}
bool operator<(ll a, mint b) {re mint(a)<(b);}
mint operator+(ll a, mint b) {re mint(a)+(b);}
mint operator-(ll a, mint b) {re mint(a)-(b);}
mint operator*(ll a, mint b) {re mint(a)*(b);}
mint operator/(ll a, mint b) {re mint(a)/(b);}

bool operator==(mint a, int b) {re a==mint(b);}
bool operator<(mint a, int b) {re a<mint(b);}
mint operator+=(mint& a, int b) {re a+=mint(b);}
mint operator-=(mint& a, int b) {re a-=mint(b);}
mint operator*=(mint& a, int b) {re a*=mint(b);}
mint operator+(mint a, int b) {re a+mint(b);}
mint operator-(mint a, int b) {re a-mint(b);}
mint operator*(mint a, int b) {re a*mint(b);}
mint operator/(mint a, int b) {re a/mint(b);}
mint operator/=(mint& a, int b) {re a/=mint(b);}

bool operator==(int a, mint b) {re mint(a)==b;}
bool operator<(int a, mint b) {re mint(a)<(b);}
mint operator+(int a, mint b) {re mint(a)+(b);}
mint operator-(int a, mint b) {re mint(a)-(b);}
mint operator*(int a, mint b) {re mint(a)*(b);}
mint operator/(int a, mint b) {re mint(a)/(b);}

//istream &operator >> (istream &is,pnt<dou> &r){is>>r.x>>r.y;return is;}
//ostream &operator << (ostream &os,pnt<dou> &r){os<<r.x<<" "<<r.y;return os;}
istream &operator >> (istream &is, mint &x)
{
	ll m;
	is >> m;
	if (m < 0 || mod <= m) {
		m %= mod; if (m < 0)m += mod;
	}
	x.n = m;
	return is;
}


ostream &operator << (ostream &os, mint &i)
{
    os << i.n;
    return os;
}


const int max_n = 1;
mint fact[max_n], factinv[max_n];
void init_f() {
	fact[0] = mint(1);
	for (int i = 0; i < max_n - 1; i++) {
		fact[i + 1] = fact[i] * mint(i + 1);
	}
	factinv[max_n - 1] = mint(1) / fact[max_n - 1];
	for (int i = max_n - 2; i >= 0; i--) {
		factinv[i] = factinv[i + 1] * mint(i + 1);
	}
}
mint comb(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[b] * factinv[a - b];
}
mint combP(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[a - b];
}

ll gcd(ll a, ll b) {
	a = abs(a); b = abs(b);
	if (a < b)swap(a, b);
	while (b) {
		ll r = a % b; a = b; b = r;
	}
	return a;
}
/* SegTreeLazy<X,M>(n,fx,fa,fm,ex,em): モノイド(集合X, 二項演算fx,fa,fm, 単位元ex,em)についてサイズnで構築
    set(int i, X x), build(): i番目の要素をxにセット。まとめてセグ木を構築する。O(n)
    update(i,x): i 番目の要素を x に更新。O(log(n))
    query(a,b):  [a,b) 全てにfxを作用させた値を取得。O(log(n))
*/
template <class X, class A> struct SegTreeLazy {
	using FX = function<X(X, X)>;
	using FAX = function<X(A,X)>;
	using FA = function<A(A, A)>;
	int n;
	FX opx;
	FAX opax;
	FA opa;
	const X ex;
	const A ea;
	vector<X> dat;
	vector<A> lazy;
	SegTreeLazy(int n_, FX opx_, X ex_, FAX opax_, FA opa_, A ea_)
		: n(), opx(opx_), opax(opax_), opa(opa_), ex(ex_), ea(ea_), dat(n_ * 4, ex), lazy(n_ * 4, ea) {
			int x = 1;
			while (n_ > x) x *= 2;
			n = x;
		}

	void set(int i, X x) { dat[i + n - 1] = x; }
	void build() {
		for (int k = n - 2; k >= 0; k--) dat[k] = opx(dat[2 * k + 1], dat[2 * k + 2]);
	}

	/* lazy eval */
	void eval(int k) {
		if (lazy[k] == ea) return;  // 更新するものが無ければ終了
		if (k < n - 1) {            // 葉でなければ子に伝搬
			lazy[k * 2 + 1] = opa(lazy[k * 2 + 1], lazy[k]);
			lazy[k * 2 + 2] = opa(lazy[k * 2 + 2], lazy[k]);
		}
		// 自身を更新
		dat[k] = opax(lazy[k],dat[k]);
		lazy[k] = ea;
	}

	void update(int a, int b, A x, int k, int l, int r) {
		eval(k);
		if (a <= l && r <= b) {  // 完全に内側の時
			lazy[k] = opa(lazy[k], x);
			eval(k);
		} else if (a < r && l < b) {                     // 一部区間が被る時
			update(a, b, x, k * 2 + 1, l, (l + r) / 2);  // 左の子
			update(a, b, x, k * 2 + 2, (l + r) / 2, r);  // 右の子
			dat[k] = opx(dat[k * 2 + 1], dat[k * 2 + 2]);
		}
	}
	void update(int a, int b, A x) { update(a, b, x, 0, 0, n); }

	X query_sub(int a, int b, int k, int l, int r) {
		eval(k);
		if (r <= a || b <= l) {  // 完全に外側の時
			return ex;
		} else if (a <= l && r <= b) {  // 完全に内側の時
			return dat[k];
		} else {  // 一部区間が被る時
			X vl = query_sub(a, b, k * 2 + 1, l, (l + r) / 2);
			X vr = query_sub(a, b, k * 2 + 2, (l + r) / 2, r);
			return opx(vl, vr);
		}
	}
	X query(int a, int b) { return query_sub(a, b, 0, 0, n); }
};
using X=mint;
struct S{
	//a*x+b;
	mint a;
	mint b;
	S(mint _a=mint(1),mint _b=mint(0)):a(_a),b(_b){;}
};
bool operator==(S a, S b) {re a.a==b.a && a.b==b.b;}
using A=S;
X opx(X x1,X x2)
{
	return x1+x2;
}
X ex=0;
X opax(A a,X x)
{
	return a.a*x+a.b;
}
A opa(A a1,A a2)
{
	A a=a1;
	a.a*=a2.a;
	a.b*=a2.a;
	a.b+=a2.b;
	return a;
}
A ea ;
//SegTreeLazy<X,A> sg(2*n,opx,ex,opax,opa,ea);
struct HLD {
    int n;
    vector<int> siz, top, dep, parent, in, out, seq;
    vector<vector<int>> adj;
    int cur;
    HLD() {}
    HLD(int n) {
        init(n);
    }
    void init(int n) {//初期化
        this->n = n;
        siz.resize(n);//部分木のサイズ
        top.resize(n);//列の先頭
        dep.resize(n);//深さ
        parent.resize(n);//親
        in.resize(n); //新しい番号
        out.resize(n);//部分木の最後の番号+1
        seq.resize(n);//order iの頂点はseq[i]
        cur = 0;
        adj.assign(n, {});//隣接リスト
    }
    void add(int u, int v) {//辺を追加
        adj[u].push_back(v);
        adj[v].push_back(u);
    }
    void work(int root = 0) {//ビルド
        top[root] = root;
        dep[root] = 0;
        parent[root] = -1;
        dfs1(root);
        dfs2(root);
    }
    void dfs1(int u) {
        if (parent[u] != -1) {
            adj[u].erase(find(adj[u].begin(), adj[u].end(), parent[u]));
	    //親を隣接リストから消す
        }
        siz[u] = 1;
        for (auto &v : adj[u]) {
            parent[v] = u;
            dep[v] = dep[u] + 1;
            dfs1(v);
            siz[u] += siz[v];
	    //adj[u][0]をheavyになるようにする
            if (siz[v] > siz[adj[u][0]]) {
                swap(v, adj[u][0]);
            }
        }
    }
    void dfs2(int u) {
        in[u] = cur++;//新しい番号を割り振る
        seq[in[u]] = u;//order in[u]の頂点はu
        for (auto v : adj[u]) {
            top[v] = v == adj[u][0] ? top[u] : v;
            dfs2(v);
        }
        out[u] = cur;
    }
    int lca(int u, int v) {
        while (top[u] != top[v]) {//同じ列でない間
            if (dep[top[u]] > dep[top[v]]) {//深い方から上る
                u = parent[top[u]];
            } else {
                v = parent[top[v]];
            }
        }
        return dep[u] < dep[v] ? u : v;
    }
    int dist(int u, int v) {
        return dep[u] + dep[v] - 2 * dep[lca(u, v)];
    }
    int jump(int u, int k) {
        if (dep[u] < k) {
            return -1;
        }
        int d = dep[u] - k;
        while (dep[top[u]] > d) {
            u = parent[top[u]];
        }
        return seq[in[u] - dep[u] + d];
    }
    bool isAncester(int u, int v) {
        return in[u] <= in[v] && in[v] < out[u];
    }
    int rootedChild(int u, int v) {
        if (u == v) {
            return u;
        }
        if (!isAncester(u, v)) {
            return parent[u];
        }
        auto it = std::upper_bound(adj[u].begin(), adj[u].end(), v, [&](int x, int y) {
            return in[x] < in[y];
        }) - 1;
        return *it;
    }
    int rootedSize(int u, int v) {
        if (u == v) {
            return n;
        }
        if (!isAncester(v, u)) {
            return siz[v];
        }
        return n - siz[rootedChild(v, u)];
    }
    int rootedLca(int a, int b, int c) {
        return lca(a, b) ^ lca(b, c) ^ lca(c, a);
    }
};
struct SegTree{
	ll n=1;vll v;
	 SegTree(ll _n){
		while(n<_n)
			n*=2;
		v.resize(n*2,0ll);
	}
	ll op(ll a,ll b){
		re a+b;
	}
	void update(ll pos,ll val){
		pos+=n-1;
		v[pos]=op(v[pos],val);
		//v[pos]=val;
		while(pos){
			pos=(pos-1)/2;
			v[pos]=op(v[pos],val);
		}
	}
	ll ran(ll l,ll r){
		re sub(l,r,0ll,0ll ,n-1);
	}
	ll sub(ll l,ll r,ll nowl,ll now,ll nowr){
		if(nowr<l||r<nowl) re 0ll;
		if(l<=nowl&&nowr<=r)re v[now];
		ll vall=sub(l,r,nowl,(now*2)+1,(nowl+nowr)/2);
		ll valr=sub(l,r,(nowl+nowr)/2+1,(now*2)+2,nowr);
		re op(vall,valr);
	}
};
void init(){
		  ios::sync_with_stdio(false);
		  cin.tie(0);
}
void solve(){
	//ge(ll,t);
	ll t=1;
	xx(t){
		sub();
	}
}
void sub() {
	ge(ll,n,m);
	vec<vll>e(n+5);
	i(m)
	{
		ge(ll,u,v);
		--u,--v;
		e[u].pub(v);
		e[v].pub(u);
	}
	vec<vll>c(15);
	vll vc(n+5);
	i(n)
	{
		ge(ll,a);
		--a;
		vc[i]=1ll<<a;
		c[a].pub(i);
	}
	vll w(15);
	i(10)
		ci(w[i]);
	vec<UF> ok;
	UF uf(n+5);
	ok.pub(uf);
	vll cst={0};
	for(ll b=1;b<(1ll<<10);++b)
	{
		ll m=0;
		ll need=0;
		ll t=b;
		for(ll i=0;t;++i)
		{
			if(t&1)
			{
				chmax(m,i);
				need+=w[i];
			}
			t>>=1;
		}
		UF uf=ok[max(0ll,b-(1ll<<m))];
		ok.pub(uf);
		cst.pub(need);
		for(ll x:c[m])
		{
			for(ll to:e[x])if(vc[to] & b)
			{
				ok[b].unite(x,to);
			}
		}
	}
	ge(ll,q);
	xx(q)
	{
		ge(ll,u,v);
		--u,--v;
		ll ans=MAX;
		for(ll b=0;b<(1ll<<10);++b)
		{
			if(ok[b].same(u,v))
			{
				chmin(ans,cst[b]);
			}
		}
		ff(ans==MAX?-1:ans);
	}
}