#include <bits/stdc++.h>
using namespace std;

//fast IO by yosupo
struct Scanner {
    FILE* fp = nullptr;
    char line[(1 << 15) + 1];
    size_t st = 0, ed = 0;
    void reread() {
        memmove(line, line + st, ed - st);
        ed -= st;
        st = 0;
        ed += fread(line + ed, 1, (1 << 15) - ed, fp);
        line[ed] = '\0';
    }
    bool succ() {
        while (true) {
            if (st == ed) {
                reread();
                if (st == ed) return false;
            }
            while (st != ed && isspace(line[st])) st++;
            if (st != ed) break;
        }
        if (ed - st <= 50) reread();
        return true;
    }
    template <class T, enable_if_t<is_same<T, string>::value, int> = 0>
    bool read_single(T& ref) {
        if (!succ()) return false;
        while (true) {
            size_t sz = 0;
            while (st + sz < ed && !isspace(line[st + sz])) sz++;
            ref.append(line + st, sz);
            st += sz;
            if (!sz || st != ed) break;
            reread();            
        }
        return true;
    }
    template <class T, enable_if_t<is_integral<T>::value, int> = 0>
    bool read_single(T& ref) {
        if (!succ()) return false;
        bool neg = false;
        if (line[st] == '-') {
            neg = true;
            st++;
        }
        ref = T(0);
        while (isdigit(line[st])) {
            ref = 10 * ref + (line[st++] - '0');
        }
        if (neg) ref = -ref;
        return true;
    }
    template <class T> bool read_single(vector<T>& ref) {
        for (auto& d : ref) {
            if (!read_single(d)) return false;
        }
        return true;
    }
    void read() {}
    template <class H, class... T> void read(H& h, T&... t) {
        bool f = read_single(h);
        assert(f);
        read(t...);
    }
    Scanner(FILE* _fp) : fp(_fp) {}
};

struct Printer {
  public:
    template <bool F = false> void write() {}
    template <bool F = false, class H, class... T>
    void write(const H& h, const T&... t) {
        if (F) write_single(' ');
        write_single(h);
        write<true>(t...);
    }
    template <class... T> void writeln(const T&... t) {
        write(t...);
        write_single('\n');
    }

    Printer(FILE* _fp) : fp(_fp) {}
    ~Printer() { flush(); }

  private:
    static constexpr size_t SIZE = 1 << 15;
    FILE* fp;
    char line[SIZE], small[50];
    size_t pos = 0;
    void flush() {
        fwrite(line, 1, pos, fp);
        pos = 0;
    }
    void write_single(const char& val) {
        if (pos == SIZE) flush();
        line[pos++] = val;
    }
    template <class T, enable_if_t<is_integral<T>::value, int> = 0>
    void write_single(T val) {
        if (pos > (1 << 15) - 50) flush();
        if (val == 0) {
            write_single('0');
            return;
        }
        if (val < 0) {
            write_single('-');
            val = -val;  // todo min
        }
        size_t len = 0;
        while (val) {
            small[len++] = char('0' + (val % 10));
            val /= 10;
        }
        reverse(small, small + len);
        memcpy(line + pos, small, len);
        pos += len;
    }
    void write_single(const string& s) {
        for (char c : s) write_single(c);
    }
    void write_single(const char* s) {
        size_t len = strlen(s);
        for (size_t i = 0; i < len; i++) write_single(s[i]);
    }
    template <class T> void write_single(const vector<T>& val) {
        auto n = val.size();
        for (size_t i = 0; i < n; i++) {
            if (i) write_single(' ');
            write_single(val[i]);
        }
    }
};

using ll=long long;
//#define int ll

#define rng(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,b) rng(i,0,b)
#define gnr(i,a,b) for(int i=int(b)-1;i>=int(a);i--)
#define per(i,b) gnr(i,0,b)
#define pb push_back
#define eb emplace_back
#define a first
#define b second
#define bg begin()
#define ed end()
#define all(x) x.bg,x.ed
#define si(x) int(x.size())
#ifdef LOCAL
#define dmp(x) cerr<<__LINE__<<" "<<#x<<" "<<x<<endl
#else
#define dmp(x) void(0)
#endif

template<class t,class u> void chmax(t&a,u b){if(a<b)a=b;}
template<class t,class u> void chmin(t&a,u b){if(b<a)a=b;}

template<class t> using vc=vector<t>;
template<class t> using vvc=vc<vc<t>>;

using pi=pair<int,int>;
using vi=vc<int>;

template<class t,class u>
ostream& operator<<(ostream& os,const pair<t,u>& p){
	return os<<"{"<<p.a<<","<<p.b<<"}";
}

template<class t> ostream& operator<<(ostream& os,const vc<t>& v){
	os<<"{";
	for(auto e:v)os<<e<<",";
	return os<<"}";
}

#define mp make_pair
#define mt make_tuple
#define one(x) memset(x,-1,sizeof(x))
#define zero(x) memset(x,0,sizeof(x))
#ifdef LOCAL
void dmpr(ostream&os){os<<endl;}
template<class T,class... Args>
void dmpr(ostream&os,const T&t,const Args&... args){
	os<<t<<" ";
	dmpr(os,args...);
}
#define dmp2(...) dmpr(cerr,__LINE__,##__VA_ARGS__)
#else
#define dmp2(...) void(0)
#endif

using uint=unsigned;
using ull=unsigned long long;

template<class t,size_t n>
ostream& operator<<(ostream&os,const array<t,n>&a){
	return os<<vc<t>(all(a));
}

template<int i,class T>
void print_tuple(ostream&,const T&){
}

template<int i,class T,class H,class ...Args>
void print_tuple(ostream&os,const T&t){
	if(i)os<<",";
	os<<get<i>(t);
	print_tuple<i+1,T,Args...>(os,t);
}

template<class ...Args>
ostream& operator<<(ostream&os,const tuple<Args...>&t){
	os<<"{";
	print_tuple<0,tuple<Args...>,Args...>(os,t);
	return os<<"}";
}

template<class t>
void print(t x,int suc=1){
	cout<<x;
	if(suc==1)
		cout<<"\n";
	if(suc==2)
		cout<<" ";
}

ll read(){
	ll i;
	cin>>i;
	return i;
}

vi readvi(int n,int off=0){
	vi v(n);
	rep(i,n)v[i]=read()+off;
	return v;
}

template<class T>
void print(const vector<T>&v,int suc=1){
	rep(i,v.size())
		print(v[i],i==int(v.size())-1?suc:2);
}

string readString(){
	string s;
	cin>>s;
	return s;
}

template<class T>
T sq(const T& t){
	return t*t;
}

//#define CAPITAL
void yes(bool ex=true){
	#ifdef CAPITAL
	cout<<"YES"<<"\n";
	#else
	cout<<"Yes"<<"\n";
	#endif
	if(ex)exit(0);
}
void no(bool ex=true){
	#ifdef CAPITAL
	cout<<"NO"<<"\n";
	#else
	cout<<"No"<<"\n";
	#endif
	if(ex)exit(0);
}
void possible(bool ex=true){
	#ifdef CAPITAL
	cout<<"POSSIBLE"<<"\n";
	#else
	cout<<"Possible"<<"\n";
	#endif
	if(ex)exit(0);
}
void impossible(bool ex=true){
	#ifdef CAPITAL
	cout<<"IMPOSSIBLE"<<"\n";
	#else
	cout<<"Impossible"<<"\n";
	#endif
	if(ex)exit(0);
}

constexpr ll ten(int n){
	return n==0?1:ten(n-1)*10;
}

const ll infLL=LLONG_MAX/3;

#ifdef int
const int inf=infLL;
#else
const int inf=INT_MAX/2-100;
#endif

int topbit(signed t){
	return t==0?-1:31-__builtin_clz(t);
}
int topbit(ll t){
	return t==0?-1:63-__builtin_clzll(t);
}
int botbit(signed a){
	return a==0?32:__builtin_ctz(a);
}
int botbit(ll a){
	return a==0?64:__builtin_ctzll(a);
}
int popcount(signed t){
	return __builtin_popcount(t);
}
int popcount(ll t){
	return __builtin_popcountll(t);
}
bool ispow2(int i){
	return i&&(i&-i)==i;
}
int mask(int i){
	return (int(1)<<i)-1;
}

bool inc(int a,int b,int c){
	return a<=b&&b<=c;
}

template<class t> void mkuni(vc<t>&v){
	sort(all(v));
	v.erase(unique(all(v)),v.ed);
}

ll rand_int(ll l, ll r) { //[l, r]
	#ifdef LOCAL
	static mt19937_64 gen;
	#else
    static random_device rd;
    static mt19937_64 gen(rd());
    #endif
    return uniform_int_distribution<ll>(l, r)(gen);
}

template<class t>
int lwb(const vc<t>&v,const t&a){
	return lower_bound(all(v),a)-v.bg;
}

using uint=unsigned;
using ull=unsigned long long;

struct modinfo{uint mod,root;};
template<modinfo const&ref>
struct modular{
	static constexpr uint const &mod=ref.mod;
	static modular root(){return modular(ref.root);}
	uint v;
	//modular(initializer_list<uint>ls):v(*ls.bg){}
	modular(ll vv=0){s(vv%mod+mod);}
	modular& s(uint vv){
		v=vv<mod?vv:vv-mod;
		return *this;
	}
	modular operator-()const{return modular()-*this;}
	modular& operator+=(const modular&rhs){return s(v+rhs.v);}
	modular&operator-=(const modular&rhs){return s(v+mod-rhs.v);}
	modular&operator*=(const modular&rhs){
		v=ull(v)*rhs.v%mod;
		return *this;
	}
	modular&operator/=(const modular&rhs){return *this*=rhs.inv();}
	modular operator+(const modular&rhs)const{return modular(*this)+=rhs;}
	modular operator-(const modular&rhs)const{return modular(*this)-=rhs;}
	modular operator*(const modular&rhs)const{return modular(*this)*=rhs;}
	modular operator/(const modular&rhs)const{return modular(*this)/=rhs;}
	modular pow(int n)const{
		modular res(1),x(*this);
		while(n){
			if(n&1)res*=x;
			x*=x;
			n>>=1;
		}
		return res;
	}
	modular inv()const{return pow(mod-2);}
	/*modular inv()const{
		int x,y;
		int g=extgcd(v,mod,x,y);
		assert(g==1);
		if(x<0)x+=mod;
		return modular(x);
	}*/
	friend modular operator+(int x,const modular&y){
		return modular(x)+y;
	}
	friend modular operator-(int x,const modular&y){
		return modular(x)-y;
	}
	friend modular operator*(int x,const modular&y){
		return modular(x)*y;
	}
	friend modular operator/(int x,const modular&y){
		return modular(x)/y;
	}
	friend ostream& operator<<(ostream&os,const modular&m){
		return os<<m.v;
	}
	friend istream& operator>>(istream&is,modular&m){
		ll x;is>>x;
		m=modular(x);
		return is;
	}
	bool operator<(const modular&r)const{return v<r.v;}
	bool operator==(const modular&r)const{return v==r.v;}
	bool operator!=(const modular&r)const{return v!=r.v;}
	explicit operator bool()const{
		return v;
	}
};

#define USE_FMT

/*
//998244353
const mint prim_root=3;
//in-place fft
//size of input must be a power of 2
void inplace_fmt(vector<mint>&f,const bool inv){
	const int n=f.size();
	const mint root=inv?prim_root.inv():prim_root;
	vc<mint> g(n);
	for(int b=n/2;b>=1;b/=2){
		mint w=root.pow((mint::base-1)/(n/b)),p=1;
		for(int i=0;i<n;i+=b*2){
			rep(j,b){
				f[i+j+b]*=p;
				g[i/2+j]=f[i+j]+f[i+b+j];
				g[n/2+i/2+j]=f[i+j]-f[i+b+j];
			}
			p*=w;
		}
		swap(f,g);
	}
	if(inv)rep(i,n)
		f[i]*=inv[n];
}*/

//size of input must be a power of 2
//output of forward fmt is bit-reversed
//output elements are in the range [0,mod*4)
//input of inverse fmt should be bit-reversed
template<class mint>
void inplace_fmt(vector<mint>&f,bool inv){
	const int n=si(f);
	static const int L=30;
	static mint g[L],ig[L],p2[L];
	if(g[0].v==0){
		rep(i,L){
			mint w=-mint::root().pow(((mint::mod-1)>>(i+2))*3);
			g[i]=w;
			ig[i]=w.inv();
			p2[i]=mint(1<<i).inv();
		}
	}
	static constexpr uint mod2=mint::mod*2;
	if(!inv){
		int b=n;
		if(b>>=1){//input:[0,mod)
			rep(i,b){
				uint x=f[i+b].v;
				f[i+b].v=f[i].v+mint::mod-x;
				f[i].v+=x;
			}
		}
		if(b>>=1){//input:[0,mod*2)
			mint p=1;
			for(int i=0,k=0;i<n;i+=b*2){
				rng(j,i,i+b){
					uint x=(f[j+b]*p).v;
					//f[j].v=(f[j].v<mint::mod?f[j].v:f[j].v-mint::mod);
					f[j+b].v=f[j].v+mint::mod-x;
					f[j].v+=x;
				}
				p*=g[__builtin_ctz(++k)];
			}
		}
		while(b){
			if(b>>=1){//input:[0,mod*3)
				mint p=1;
				for(int i=0,k=0;i<n;i+=b*2){
					rng(j,i,i+b){
						uint x=(f[j+b]*p).v;
						//f[j].v=(f[j].v<mint::mod?f[j].v:f[j].v-mint::mod);
						f[j+b].v=f[j].v+mint::mod-x;
						f[j].v+=x;
					}
					p*=g[__builtin_ctz(++k)];
				}
			}
			if(b>>=1){//input:[0,mod*4)
				mint p=1;
				for(int i=0,k=0;i<n;i+=b*2){
					rng(j,i,i+b){
						uint x=(f[j+b]*p).v;
						f[j].v=(f[j].v<mod2?f[j].v:f[j].v-mod2);
						f[j+b].v=f[j].v+mint::mod-x;
						f[j].v+=x;
					}
					p*=g[__builtin_ctz(++k)];
				}
			}
		}
	}else{
		int b=1;
		if(b<n/2){//input:[0,mod)
			mint p=1;
			for(int i=0,k=0;i<n;i+=b*2){
				rng(j,i,i+b){
					ull x=f[j].v+mint::mod-f[j+b].v;
					f[j].v+=f[j+b].v;
					f[j+b].v=x*p.v%mint::mod;
				}
				p*=ig[__builtin_ctz(++k)];
			}
			b<<=1;
		}
		for(;b<n/2;b<<=1){
			mint p=1;
			for(int i=0,k=0;i<n;i+=b*2){
				rng(j,i,i+b/2){//input:[0,mod*2)
					ull x=f[j].v+mod2-f[j+b].v;
					f[j].v+=f[j+b].v;
					f[j].v=(f[j].v)<mod2?f[j].v:f[j].v-mod2;
					f[j+b].v=x*p.v%mint::mod;
				}
				rng(j,i+b/2,i+b){//input:[0,mod)
					ull x=f[j].v+mint::mod-f[j+b].v;
					f[j].v+=f[j+b].v;
					//f[j].v=(f[j].v)<mod2?f[j].v:f[j].v-mod2;
					f[j+b].v=x*p.v%mint::mod;
				}
				p*=ig[__builtin_ctz(++k)];
			}
		}
		if(b<n){//input:[0,mod*2)
			rep(i,b){
				uint x=f[i+b].v;
				f[i+b].v=f[i].v+mod2-x;
				f[i].v+=x;
			}
		}
		mint z=p2[__lg(n)];
		rep(i,n)f[i]*=z;
	}
}

/*
template<class mint>
vc<mint> multiply(vc<mint> x,const vc<mint>&y,bool same=false){
	int n=si(x)+si(y)-1;
	int s=1;
	while(s<n)s*=2;
	x.resize(s);inplace_fmt(x,false);
	if(!same){
		vc<mint> z(s);
		rep(i,si(y))z[i]=y[i];
		inplace_fmt(z,false);
		rep(i,s)x[i]*=z[i];
	}else{
		rep(i,s)x[i]*=x[i];
	}
	inplace_fmt(x,true);x.resize(n);
	return x;
}
*/

//59501818244292734739283969=5.95*10^25 までの値を正しく計算
//最終的な列の大きさが 2^24 までなら動く
//最終的な列の大きさが 2^20 以下のときは，下の 3 つの素数を使ったほうが速い（は？）
//VERIFY: yosupo
namespace arbitrary_convolution{
	//constexpr modinfo base0{167772161,3};//2^25 * 5 + 1
	//constexpr modinfo base1{469762049,3};//2^26 * 7 + 1
	//constexpr modinfo base2{754974721,11};//2^24 * 45 + 1
	extern constexpr modinfo base0{1045430273,3};//2^20 * 997 + 1
	extern constexpr modinfo base1{1051721729,6};//2^20 * 1003 + 1
	extern constexpr modinfo base2{1053818881,7};//2^20 * 1005 + 1
	using mint0=modular<base0>;
	using mint1=modular<base1>;
	using mint2=modular<base2>;
	template<class t,class mint>
	vc<t> sub(const vc<mint>&x,const vc<mint>&y,bool same=false){
		int n=si(x)+si(y)-1;
		int s=1;
		while(s<n)s*=2;
		vc<t> z(s);rep(i,si(x))z[i]=x[i].v;
		inplace_fmt(z,false);
		if(!same){
			vc<t> w(s);rep(i,si(y))w[i]=y[i].v;
			inplace_fmt(w,false);
			rep(i,s)z[i]*=w[i];
		}else{
			rep(i,s)z[i]*=z[i];
		}
		inplace_fmt(z,true);z.resize(n);
		return z;
	}
	template<class mint>
	vc<mint> multiply(const vc<mint>&x,const vc<mint>&y,bool same=false){
		auto d0=sub<mint0>(x,y,same);
		auto d1=sub<mint1>(x,y,same);
		auto d2=sub<mint2>(x,y,same);
		int n=si(d0);
		vc<mint> res(n);
		static const mint1 r01=mint1(mint0::mod).inv();
		static const mint2 r02=mint2(mint0::mod).inv();
		static const mint2 r12=mint2(mint1::mod).inv();
		static const mint2 r02r12=r02*r12;
		static const mint w1=mint(mint0::mod);
		static const mint w2=w1*mint(mint1::mod);
		rep(i,n){
			ull a=d0[i].v;
			ull b=(d1[i].v+mint1::mod-a)*r01.v%mint1::mod;
			ull c=((d2[i].v+mint2::mod-a)*r02r12.v+(mint2::mod-b)*r12.v)%mint2::mod;
			res[i].v=(a+b*w1.v+c*w2.v)%mint::mod;
		}
		return res;
	}
}
using arbitrary_convolution::multiply;

//constexpr modinfo base{998244353,3};
extern constexpr modinfo base{1000000007,0};
using mint=modular<base>;

/*signed main(){
	//cin.tie(0);
	//ios::sync_with_stdio(0);
	//cout<<fixed<<setprecision(20);
	
	Scanner sc(stdin);
	Printer pr(stdout);
	
	int n,m;
	sc.read(n,m);
	vc<mint> a(n),b(m);
	
	rep(i,n)sc.read(a[i].v);
	rep(i,m)sc.read(b[i].v);
	
	auto c=multiply(a,b);
	
	rep(i,c.size()){
		pr.write(c[i].v);
		pr.write(i<si(c)-1?' ':'\n');
	}
}*/
typedef long long ll;
typedef pair<ll,ll> P;

#define fr first
#define sc second

const ll MOD=1000000007;
ll modpow(ll x,ll k,ll mod=MOD){
	if(k==0)return 1;
	ll ret=modpow(x,k/2,mod);
	ret*=ret; ret%=mod;
	if(k%2==1){
		ret*=x; ret%=mod;
	}
	return ret;
}

template <const int p=998244353,int t=20>
struct CONV{
	ll a[(1<<t)+2];
	ll b[(1<<t)+2];
	ll c[(1<<t)+2];
	ll r[(1<<t)+2];
	CONV(){
		for(int i=0;i<(1<<t)+2;i++){
			a[i]=b[i]=c[i]=0;
		}
		int tt=0;
		int x=p-1;
		while(x%2==0){
			tt++;
			x/=2;
		}
		r[1]=1;
		while(1){
			r[1]++;
			if(modpow(r[1],1<<(tt-1),p)==p-1)break;
		}
		for(int i=0;i<tt-t;i++){
			r[1]*=r[1];
			r[1]%=p;
		}
		r[0]=1;
		for(int i=2;i<(1<<t)+2;i++){
			r[i]=r[i-1]*r[1];
			r[i]%=p;
		}
	}
	void init(int tt){
		for(int i=0;i<(1<<tt)+2;i++){
			a[i]=b[i]=c[i]=0;
		}
	}
	ll coef_a[(1<<t)+2];
	ll coef_b[(1<<t)+2];
	void DFT(ll* f,ll* g,int tt){
		g[0]=0;
		for(int i=0;i<tt;i++){
			for(int j=0;j<(1<<i);j++){
				g[j+(1<<i)]=g[j]+(1<<(tt-1-i));
			}
		}
		for(int i=0;i<(1<<tt);i++){
			g[i]=f[g[i]];
		}
		for(int i=0;i<tt;i++){
			for(int j=0;j<(1<<tt);j++){
				if((j>>i)&1)continue;
				if(g[j+(1<<i)]==0){
					g[j+(1<<i)]=g[j];
					continue;
				}
				g[j+(1<<i)]*=r[(j&((1<<i)-1))<<(t-i-1)];
				g[j+(1<<i)]%=p;
				g[j]+=g[j+(1<<i)];
				if(g[j]>=p)g[j]-=p;
				g[j+(1<<i)]=g[j]+2*(p-g[j+(1<<i)]);
				while(g[j+(1<<i)]>=p)g[j+(1<<i)]-=p;
			}
		}
	}
	void inv_DFT(ll* f,ll* g,int tt){
		g[0]=0;
		for(int i=0;i<tt;i++){
			for(int j=0;j<(1<<i);j++){
				g[j+(1<<i)]=g[j]+(1<<(tt-1-i));
			}
		}
		for(int i=0;i<(1<<tt);i++){
			g[i]=f[g[i]];
		}
		for(int i=0;i<tt;i++){
			for(int j=0;j<(1<<tt);j++){
				if((j>>i)&1)continue;
				if(g[j+(1<<i)]==0){
					g[j+(1<<i)]=g[j];
					continue;
				}
				g[j+(1<<i)]*=r[(1<<t)-((j&((1<<i)-1))<<(t-i-1))];
				g[j+(1<<i)]%=p;
				g[j]+=g[j+(1<<i)];
				if(g[j]>=p)g[j]-=p;
				g[j+(1<<i)]=g[j]+2*(p-g[j+(1<<i)]);
				while(g[j+(1<<i)]>=p)g[j+(1<<i)]-=p;
			}
		}
	}
	void run(int tt){
		DFT(a,coef_a,tt);
		DFT(b,coef_b,tt);
		for(int i=0;i<(1<<tt);i++){
			coef_a[i]*=coef_b[i];
			coef_a[i]%=p;
		}
		inv_DFT(coef_a,coef_b,tt);
		ll inv=modpow(1<<tt,p-2,p);
		for(int i=0;i<(1<<tt);i++){
			c[i]=coef_b[i]*inv;
			c[i]%=p;
		}
	}
};

inline ll CRT(ll m2,ll a1,ll a2,ll s1){
	//x=a1(mod m1), x=a2(mod m2), s1*m1=1(mod m2)
	//x=ret*m1+a1 (mod m1*m2)
	return (a2-a1%m2+m2)*s1%m2;
}

ll s1=modpow(1045430273,1051721729-2,1051721729);
ll s2=modpow(1045430273*1051721729LL%1053818881,1053818881-2,1053818881);
ll pp=1045430273*1051721729LL%1000000007;

template<int p=1000000007,int t=20>
struct CONV_arb{
	ll a[(1<<t)+2];
	ll b[(1<<t)+2];
	ll c[(1<<t)+2];
	const ll p1=1045430273;
	const ll p2=1051721729;
	const ll p3=1053818881;
	void init(int tt){
		for(int i=0;i<(1<<tt)+2;i++){
			a[i]=b[i]=0;
		}
	}
	void run(int tt){
		static CONV<1045430273,14> conv1;
		static CONV<1051721729,14> conv2;
		static CONV<1053818881,14> conv3;
		//conv1.init(tt);
		//conv2.init(tt);
		//conv3.init(tt);
		for(int i=0;i<(1<<tt);i++){
			conv1.a[i]=conv2.a[i]=conv3.a[i]=a[i];
			conv1.b[i]=conv2.b[i]=conv3.b[i]=b[i];
		}
		conv1.run(tt);
		conv2.run(tt);
		conv3.run(tt);
		for(int i=0;i<(1<<tt);i++){
			ll x=conv1.c[i]+CRT(p2,conv1.c[i],conv2.c[i],s1)*p1;
			ll y=CRT(p3,x,conv3.c[i],s2);
			y*=pp;
			c[i]=x+y;
			c[i]%=p;
		}
	}
};

ll fac[5002];
ll fac_inv[5002];
ll inv[5002];
void init(){
	fac[0]=fac_inv[0]=1;
	for(int i=1;i<5002;i++){
		fac[i]=fac[i-1]*i;
		fac[i]%=MOD;
		fac_inv[i]=modpow(fac[i],MOD-2);
	}
	for(int i=0;i<5002;i++){
		inv[i]=modpow(i,MOD-2);
	}
}

int n;
vector<int> G[5002];
int cnt[5002];
ll dp[5002][5002];
ll memo[5002];

CONV_arb<1000000007,14> conv;

void dfs(int v,int p){
	cnt[v]=1;
	for(int i=0;i<5002;i++){
		dp[v][i]=0;
	}
	dp[v][1]=1;
	for(int u: G[v]){
		if(u==p)continue;
		dfs(u,v);
		for(int i=0;i<=cnt[v]+cnt[u];i++){
			memo[i]=0;
		}
		if(min(cnt[u],cnt[v])<=40){
			for(int i=0;i<=min(cnt[v],n-cnt[v]);i++){
				if(dp[v][i]==0)continue;
				for(int j=1;j<=min(cnt[u],n-cnt[u]);j++){
					if(dp[u][j]==0)continue;
					ll x=dp[v][i]*dp[u][j];
					x%=MOD;
					for(int k=0;k<=min(i,j);k++){
						memo[i+j-2*k]+=x;
						if(memo[i+j-2*k]>=MOD)memo[i+j-2*k]-=MOD;
						x*=(i-k)*(j-k);
						x%=MOD;
						x*=inv[k+1];
						x%=MOD;
					}
				}
			}
		}
		else {
			int cc=min(cnt[u]+cnt[v],n-cnt[u]-cnt[v]);
			for(int k=0;k<=min(cnt[v],cnt[u]);k++){
				int tt=0;
				while((1<<tt)<=min(2*cc,min(cnt[v],n-cnt[v])+min(cnt[u],n-cnt[u])-2*k))tt++;
				if(tt!=0)tt--;
				conv.init(tt);
				for(int i=k;i<=min(cc+k,min(cnt[v],n-cnt[v]));i++){
					if(dp[v][i]==0)continue;
					conv.a[(i-k)/2]=dp[v][i];
					conv.a[(i-k)/2]*=fac[i]; conv.a[(i-k)/2]%=MOD;
					conv.a[(i-k)/2]*=fac_inv[i-k]; conv.a[(i-k)/2]%=MOD;
				}
				for(int j=max(1,k);j<=min(cc+k,min(cnt[u],n-cnt[u]));j++){
					if(dp[u][j]==0)continue;
					conv.b[(j-k)/2]=dp[u][j];
					conv.b[(j-k)/2]*=fac[j]; conv.b[(j-k)/2]%=MOD;
					conv.b[(j-k)/2]*=fac_inv[j-k]; conv.b[(j-k)/2]%=MOD;
					conv.b[(j-k)/2]*=fac_inv[k]; conv.b[(j-k)/2]%=MOD;
				}
				//conv.run(tt);
				vc<mint> a(1<<tt),b(1<<tt);
				for(int i=0;i<(1<<tt);i++)a[i].v=conv.a[i];
				for(int i=0;i<(1<<tt);i++)b[i].v=conv.b[i];
				while(a.size()>1&&a[a.size()-1].v==0)a.pop_back();
				while(b.size()>1&&b[b.size()-1].v==0)b.pop_back();
				auto c=multiply(a,b);
				int x=((cnt[v]-k)&1)+((cnt[u]-k)&1);
				for(int i=0;i<min((1<<tt),(int)c.size());i++){
					if(2*i+x>=5002)break;
					memo[2*i+x]+=c[i].v;
					if(memo[2*i+x]>=MOD)memo[2*i+x]-=MOD;
				}
			}
		}
		for(int i=0;i<=cnt[v]+cnt[u];i++){
			dp[v][i]=memo[i];
		}
		cnt[v]+=cnt[u];
	}
}

ll CNT[5002];
ll dfs2(int v,int p){
	CNT[v]=1;
	ll ret=0;
	for(int u: G[v]){
		if(u==p)continue;
		ret+=dfs2(u,v);
		ll x=CNT[v];
		ll y=CNT[u];
		ll k=min(CNT[u],CNT[v]);
		ret+=k*x*y;
		ret-=k*(k-1)*(x+y)/2;
		ret+=k*(k-1)*(2*k-1)/6;
		CNT[v]+=CNT[u];
	}
}

int main(){
	init();
	scanf("%d",&n);
	for(int i=0;i<n-1;i++){
		int a,b;
		scanf("%d%d",&a,&b);
		G[a].push_back(b);
		G[b].push_back(a);
	}
	srand((unsigned)time(NULL));
	int root=1;
	ll MIN=1000000000000;
	for(int i=1;i<=n;i++){
		ll x=dfs2(i,0);
		if(x<MIN){
			MIN=x;
			root=i;
		}
	}
	dfs(root,0);
	cout<<dp[root][0]<<endl;
	int t_end=clock();
}




Measured memory_bytes: 197120