#ifndef LOCAL
#pragma GCC optimize ("Ofast")
#pragma GCC optimize ("unroll-loops")
#endif

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

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

bool dbg=false;

#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> bool chmax(t&a,u b){if(a<b){a=b;return true;}else return false;}
template<class t,class u> bool chmin(t&a,u b){if(b<a){a=b;return true;}else return false;}

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));
}

ll rand_int(ll l, ll r) { //[l, r]
	//#ifdef LOCAL
	static mt19937_64 gen;
	/*#else
	static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
	#endif*/
	return uniform_int_distribution<ll>(l, r)(gen);
}

ll rand_int(ll k){ //[0,k)
	return rand_int(0,k-1);
}
string rand_string(int n,char lw,char up){
	string s(n,'?');
	rep(i,n)s[i]=rand_int(lw,up);
	return s;
}

int current_run_id,run_batch_size=1000;
int calc_random_limit(){
	return current_run_id/run_batch_size+1;
}
#ifndef int
void generate_single(int&a){
	a=rand_int(1,calc_random_limit());
}
#endif
void generate_single(ll&a){
	a=rand_int(1,calc_random_limit());
}
void generate_single(string&a){
	int n;generate_single(n);
	a=rand_string(n,'a','b');
}
//https://trap.jp/post/1224/
template<class... Args>
void input(Args&... a){
	if(dbg){
		(generate_single(a),...);
	}else{
		(cin >> ... >> a);
	}
}
#define INT(...) int __VA_ARGS__;input(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__;input(__VA_ARGS__)
#define ULL(...) ull __VA_ARGS__;input(__VA_ARGS__)
#define STR(...) string __VA_ARGS__;input(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__;input(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__;input(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__;input(__VA_ARGS__)
#define overload3(a,b,c,d,...) d
#define VI2(name,size) vi name(size);rep(i,size)input(name[i]);
#define VI3(name,size,offset) vi name(size);rep(i,size)input(name[i]),name[i]+=offset;
#define VI(...) overload3(__VA_ARGS__,VI3,VI2)(__VA_ARGS__)

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<<"}";
}

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;
}

pi readpi(int off=0){
	int a,b;cin>>a>>b;
	return pi(a+off,b+off);
}

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

template<class t,class u>
void print_single(const pair<t,u>&p,int suc=1){
	print_single(p.a,2);
	print_single(p.b,suc);
}

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

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

template<class T,size_t N>
void print_single(const array<T,N>&v,int suc=1){
	rep(i,N)
		print_single(v[i],i==int(N)-1?suc:2);
}

template<class T>
void print(const T&t){
	print_single(t);
}

template<class T,class ...Args>
void print(const T&t,const Args&...args){
	print_single(t,2);
	print(args...);
}

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

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

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

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 topbit(ull 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 botbit(ull a){
	return a==0?64:__builtin_ctzll(a);
}
int popcount(signed t){
	return __builtin_popcount(t);
}
int popcount(ll t){
	return __builtin_popcountll(t);
}
int popcount(ull t){
	return __builtin_popcountll(t);
}
int bitparity(ll t){
	return __builtin_parityll(t);
}
bool ispow2(int i){
	return i&&(i&-i)==i;
}
ll mask(int i){
	return (ll(1)<<i)-1;
}
ull umask(int i){
	return (ull(1)<<i)-1;
}
ll minp2(ll n){
	if(n<=1)return 1;
	else return ll(1)<<(topbit(n-1)+1);
}

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

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

template<class t> bool isuni(vc<t> v){
	int s=si(v);
	mkuni(v);
	return si(v)==s;
}

template<class t>
void myshuffle(vc<t>&a){
	rep(i,si(a))swap(a[i],a[rand_int(0,i)]);
}

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

vvc<int> readGraph(int n,int m){
	vvc<int> g(n);
	rep(i,m){
		int a,b;
		cin>>a>>b;
		//sc.read(a,b);
		a--;b--;
		g[a].pb(b);
		g[b].pb(a);
	}
	return g;
}

vvc<int> readTree(int n){
	return readGraph(n,n-1);
}

template<class t>
vc<t> presum(const vc<t>&a){
	vc<t> s(si(a)+1);
	rep(i,si(a))s[i+1]=s[i]+a[i];
	return s;
}
vc<ll> presum(const vi&a){
	vc<ll> s(si(a)+1);
	rep(i,si(a))s[i+1]=s[i]+a[i];
	return s;
}
//BIT で数列を管理するときに使う (CF850C)
template<class t>
vc<t> predif(vc<t> a){
	gnr(i,1,si(a))a[i]-=a[i-1];
	return a;
}
template<class t>
vvc<ll> imos(const vvc<t>&a){
	int n=si(a),m=si(a[0]);
	vvc<ll> b(n+1,vc<ll>(m+1));
	rep(i,n)rep(j,m)
		b[i+1][j+1]=b[i+1][j]+b[i][j+1]-b[i][j]+a[i][j];
	return b;
}

//verify してないや
void transvvc(int&n,int&m){
	swap(n,m);
}
template<class t,class... Args>
void transvvc(int&n,int&m,vvc<t>&a,Args&...args){
	assert(si(a)==n);
	vvc<t> b(m,vi(n));
	rep(i,n){
		assert(si(a[i])==m);
		rep(j,m)b[j][i]=a[i][j];
	}
	a.swap(b);
	transvvc(n,m,args...);
}
//CF854E
void rotvvc(int&n,int&m){
	swap(n,m);
}
template<class t,class... Args>
void rotvvc(int&n,int&m,vvc<t>&a,Args&...args){
	assert(si(a)==n);
	vvc<t> b(m,vi(n));
	rep(i,n){
		assert(si(a[i])==m);
		rep(j,m)b[m-1-j][i]=a[i][j];
	}
	a.swap(b);
	rotvvc(n,m,args...);
}

//ソートして i 番目が idx[i]
//CF850C
template<class t>
vi sortidx(const vc<t>&a){
	int n=si(a);
	vi idx(n);iota(all(idx),0);
	sort(all(idx),[&](int i,int j){return a[i]<a[j];});
	return idx;
}
//vs[i]=a[idx[i]]
//例えば sortidx で得た idx を使えば単にソート列になって返ってくる
//CF850C
template<class t>
vc<t> a_idx(const vc<t>&a,const vi&idx){
	int n=si(a);
	assert(si(idx)==n);
	vc<t> vs(n);
	rep(i,n)vs[i]=a[idx[i]];
	return vs;
}
//CF850C
vi invperm(const vi&p){
	int n=si(p);
	vi q(n);
	rep(i,n)q[p[i]]=i;
	return q;
}

template<class t,class s=t>
s SUM(const vc<t>&a){
	return accumulate(all(a),s(0));
}
template<class t,size_t K,class s=t>
s SUM(const array<t,K>&a){
	return accumulate(all(a),s(0));
}

template<class t>
t MAX(const vc<t>&a){
	return *max_element(all(a));
}

template<class t>
pair<t,int> MAXi(const vc<t>&a){
	auto itr=max_element(all(a));
	return mp(*itr,itr-a.bg);
}

template<class A>
auto MIN(const A&a){
	return *min_element(all(a));
}

template<class t>
pair<t,int> MINi(const vc<t>&a){
	auto itr=min_element(all(a));
	return mp(*itr,itr-a.bg);
}

vi vid(int n){
	vi res(n);iota(all(res),0);
	return res;
}

template<class S>
void soin(S&s){
	sort(all(s));
}

template<class S,class F>
void soin(S&s,F&&f){
	sort(all(s),forward<F>(f));
}

template<class S>
S soout(S s){
	soin(s);
	return s;
}

template<class S>
void rein(S&s){
	reverse(all(s));
}

template<class S>
S reout(S s){
	rein(s);
	return s;
}

template<class t,class u>
pair<t,u>&operator+=(pair<t,u>&a,pair<t,u> b){
	a.a+=b.a;a.b+=b.b;return a;}
template<class t,class u>
pair<t,u>&operator-=(pair<t,u>&a,pair<t,u> b){
	a.a-=b.a;a.b-=b.b;return a;}
template<class t,class u>
pair<t,u> operator+(pair<t,u> a,pair<t,u> b){return mp(a.a+b.a,a.b+b.b);}
template<class t,class u>
pair<t,u> operator-(pair<t,u> a,pair<t,u> b){return mp(a.a-b.a,a.b-b.b);}
template<class t,class u>
pair<t,u> operator-(pair<t,u> a){return mp(-a.a,-a.b);}
template<class t,class u>
istream&operator>>(istream&is,pair<t,u>&a){
	return is>>a.a>>a.b;
}

template<class t>
t gpp(vc<t>&vs){
	assert(si(vs));
	t res=move(vs.back());
	vs.pop_back();
	return res;
}

template<class t,class u>
void pb(vc<t>&a,const vc<u>&b){
	a.insert(a.ed,all(b));
}

template<class t,class...Args>
vc<t> cat(vc<t> a,Args&&...b){
	(pb(a,forward<Args>(b)),...);
	return a;
}

template<class t,class u>
vc<t>& operator+=(vc<t>&a,u x){
	for(auto&v:a)v+=x;
	return a;
}

template<class t,class u>
vc<t> operator+(vc<t> a,u x){
	return a+=x;
}

template<class t>
vc<t> operator+(const vc<t>&a,const vc<t>&b){
	vc<t> c(max(si(a),si(b)));
	rep(i,si(a))c[i]+=a[i];
	rep(i,si(b))c[i]+=b[i];
	return c;
}

template<class t,class u>
vc<t>& operator-=(vc<t>&a,u x){
	for(auto&v:a)v-=x;
	return a;
}

template<class t,class u>
vc<t>& operator-(vc<t> a,u x){
	return a-=x;
}

template<class t,class u>
void remval(vc<t>&a,const u&v){
	a.erase(remove(all(a),v),a.ed);
}
//消した要素の個数を返してくれる
//UCUP 2-8-F
template<class t,class F>
int remif(vc<t>&a,F f){
	auto itr=remove_if(all(a),f);
	int res=a.ed-itr;
	a.erase(itr,a.ed);
	return res;
}

template<class VS,class u>
void fila(VS&vs,const u&a){
	fill(all(vs),a);
}

template<class t,class u>
int findid(const vc<t>&vs,const u&a){
	auto itr=find(all(vs),a);
	if(itr==vs.ed)return -1;
	else return itr-vs.bg;
}

template<class t>
void rtt(vc<t>&vs,int i){
	rotate(vs.bg,vs.bg+i,vs.ed);
}

//Multiuni2023-8 C
//f(lw)=false,...,f(n-1)=false,f(n)=true,...,f(up)=true,
//のときに n を返す
template<class F>
int find_min_true(int lw,int up,F f){
	while(up-lw>1){
		const int mid=(lw+up)/2;
		if(f(mid))up=mid;
		else lw=mid;
	}
	return up;
}
//f(lw)=true,f(up)=false
template<class F>
int find_max_true(int lw,int up,F f){
	while(up-lw>1){
		const int mid=(lw+up)/2;
		if(f(mid))lw=mid;
		else up=mid;
	}
	return lw;
}

//mint107 は verify してねえ
//#define DYNAMIC_MOD

struct modinfo{uint mod,root;
#ifdef DYNAMIC_MOD
constexpr modinfo(uint m,uint r):mod(m),root(r),im(0){set_mod(m);}
ull im;
constexpr void set_mod(uint m){
	mod=m;
	im=ull(-1)/m+1;
}
uint product(uint a,uint b)const{
	ull z=ull(a)*b;
	uint x=((unsigned __int128)z*im)>>64;
	uint v=uint(z)-x*mod;
	return v<mod?v:v+mod;
}
#endif
};
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){
		#ifndef DYNAMIC_MOD
		v=ull(v)*rhs.v%mod;
		#else
		v=ref.product(v,rhs.v);
		#endif
		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(ll n)const{
		if(n<0)return inv().pow(-n);
		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<ll>(v,mod,x,y);
		assert(g==1);
		if(x<0)x+=mod;
		return modular(x);
	}*/
	friend modular operator+(ll x,const modular&y){
		return modular(x)+y;
	}
	friend modular operator-(ll x,const modular&y){
		return modular(x)-y;
	}
	friend modular operator*(ll x,const modular&y){
		return modular(x)*y;
	}
	friend modular operator/(ll 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;
	}
};

#ifndef DYNAMIC_MOD
//extern constexpr modinfo base{998244353,3};
extern constexpr modinfo base{1000000007,0};
//extern constexpr modinfo base{2147483579,1689685080};//2^31 未満の最大の安全素数
//modinfo base{1,0};
#ifdef USE_GOOD_MOD
static_assert(base.mod==998244353);
#endif
#else
modinfo base(1,0);
extern constexpr modinfo base107(1000000007,0);
using mint107=modular<base107>;
#endif
using mint=modular<base>;
extern constexpr modinfo base7{7,0};
using mint7=modular<base7>;

mint parity(int i){
	return i%2==0?1:-1;
}

#ifdef LOCAL
const int vmax=10010;
#else
const int vmax=(1<<21)+10;
#endif
mint fact[vmax],finv[vmax],invs[vmax];
void initfact(){
	fact[0]=1;
	rng(i,1,vmax){
		fact[i]=fact[i-1]*i;
	}
	finv[vmax-1]=fact[vmax-1].inv();
	for(int i=vmax-2;i>=0;i--){
		finv[i]=finv[i+1]*(i+1);
	}
	for(int i=vmax-1;i>=1;i--){
		invs[i]=finv[i]*fact[i-1];
	}
}
mint choose(int n,int k){
	return inc(0,k,n)?fact[n]*finv[n-k]*finv[k]:0;
}
mint binom(int a,int b){
	return 0<=a&&0<=b?fact[a+b]*finv[a]*finv[b]:0;
}
mint catalan(int n){
	return binom(n,n)-(n-1>=0?binom(n-1,n+1):0);
}
//対角線を超えず (x,y) に至る方法の数
mint catalan(int x,int y){
	assert(y<=x);
	return binom(x,y)-binom(x+1,y-1);
}
//y=x+c を超えず (x,y) に至る方法の数
mint catalan(int x,int y,int c){
	assert(y<=x+c);
	return binom(x,y)-binom(x+c+1,y-c-1);
}

/*
const int vmax=610;
mint fact[vmax+1],binbuf[vmax+1][vmax+1];
mint choose(int n,int k){
	return 0<=k&&k<=n?binbuf[n-k][k]:0;
}
mint binom(int a,int b){
	return 0<=a&&0<=b?binbuf[a][b]:0;
}
void initfact(int n){
	fact[0]=1;
	rep(i,n)fact[i+1]=fact[i]*(i+1);
	rep(i,n+1)rep(j,n+1){
		if(i==0&&j==0){
			binbuf[i][j]=1;
		}else{
			binbuf[i][j]=0;
			if(i)binbuf[i][j]+=binbuf[i-1][j];
			if(j)binbuf[i][j]+=binbuf[i][j-1];
		}
	}
}
*/

mint p2[vmax],p2inv[vmax];
void initp2(){
	p2[0]=1;
	rep(i,vmax-1)p2[i+1]=p2[i]*2;
	p2inv[vmax-1]=p2[vmax-1].inv();
	per(i,vmax-1)p2inv[i]=p2inv[i+1]*2;
}


template<class F>
void array_rec(int n,int m,F f){
	vi a(n);
	function<void(int)> rec=[&](int i)->void{
		if(i==n)f(a);
		else{
			rep(nx,m){
				a[i]=nx;
				rec(i+1);
			}
		}
	};
	rec(0);
}

const int nmax=10005;
mint way[nmax][7];
mint7 pw[7][7];
const int T=3;
//vvc<int> lookup[1<<7];
vvc<pi> lookup[1<<7];

mint x[7][nmax][7];
mint y[7][7][nmax][7][7];

mint wA[nmax][343];
mint wB[nmax][343];

void init(){
	way[0][0]=1;
	rep(i,nmax-1){
		rep(j,7){
			way[i+1][j]+=way[i][j];
			way[i+1][(j+1)%7]+=way[i][j];
		}
	}
	rep(i,7)rep(j,7)pw[i][j]=mint7(i).pow(j);
	
	rep(bit,1<<7)if((bit&1)==0&&popcount(bit)>=T){
		vi pos;
		rep(i,7)if(bit&1<<i)pos.pb(i);
		int len=si(pos);
		
		int s=1;rep(_,len)s*=7;
		lookup[bit].resize(s);
		
		/*array_rec(6,7,[&](vi a){
			int idx=0;
			per(i,6){
				idx=idx*7+a[i];
			}
			int to=0;
			per(i,len){
				mint7 sum=0;
				rep(j,6)sum+=pw[pos[i]][j]*a[j];
				to=to*7+(sum.v);
			}
			lookup[bit][to].pb(idx);
		});*/
		vi a(6);
		vc<mint7> sum(len);
		auto dfs=[&](auto self,int j)->void{
			if(j==6){
				int idx=0;
				per(i,6){
					idx=idx*7+a[i];
				}
				int to=0;
				per(i,len){
					to=to*7+(sum[i].v);
				}
				//lookup[bit][to].pb(idx);
				lookup[bit][to].eb(idx%343,idx/343);
			}else{
				rep(v,7){
					a[j]=v;
					rep(i,len)sum[i]+=pw[pos[i]][j]*v;
					self(self,j+1);
					rep(i,len)sum[i]-=pw[pos[i]][j]*v;
				}
			}
		};
		dfs(dfs,0);
	}
	
	/*rep(bit,1<<7)if((bit&1)==0&&popcount(bit)<T){
		//1
		rng(a,1,6)
	}*/
	rng(a,1,7){
		x[a][1][0]=1;
		rng(i,1,nmax-1){
			rep(j,7){
				x[a][i+1][j]+=x[a][i][j];
				x[a][i+1][(j+pw[a][i%6]).v]+=x[a][i][j];
			}
		}
	}
	rng(a,1,7)rng(b,a+1,7){
		y[a][b][1][0][0]=1;
		rng(i,1,nmax-1){
			rep(j,7)rep(k,7){
				y[a][b][i+1][j][k]+=y[a][b][i][j][k];
				y[a][b][i+1][(j+pw[a][i%6]).v][(k+pw[b][i%6]).v]+=y[a][b][i][j][k];
			}
		}
	}
	
	rng(i,1,nmax)rep(a,7)rep(b,7)rep(c,7){
		int az=(i+5)/6-1;
		int bz=(i+4)/6;
		int cz=(i+3)/6;
		wA[i][a+b*7+c*49]=way[az][a]*way[bz][b]*way[cz][c];
	}
	rng(i,1,nmax)rep(a,7)rep(b,7)rep(c,7){
		int az=(i+2)/6;
		int bz=(i+1)/6;
		int cz=(i+0)/6;
		wB[i][a+b*7+c*49]=way[az][a]*way[bz][b]*way[cz][c];
	}
	//cerr<<"Init Done"<<endl;
}
void slv(){
	STR(raw);
	if(raw=="-1"){
		raw.clear();
		rep(i,10000){
			raw.pb('1');
		}
	}
	int n=si(raw);
	vi s(n);
	rep(i,n)s[i]=raw[n-1-i]-'0';
	mint ans;
	
	mint7 fix[7];
	auto add=[&](int i,mint7 w){
		rng(k,1,7)fix[k]+=pw[k][i%6]*w;
	};
	
	add(0,1);
	per(i,n){
		int mx=s[i];
		if(i==0)mx++;
		rep(v,mx){//fix digit i or above
			add(i,v);
			
			if(i==0){
				if(v==1){
					add(0,-1);
					bool ok=true;
					rng(k,1,7)if(fix[k]==0)ok=false;
					if(ok)ans+=1;
					add(0,1);
				}
			}else{
				//digit [1,i) で
				//fix + 残りがいい感じになるようにする方法は何通りあるか？
				//包除
				rep(bit,1<<7)if((bit&1)==0){
					if(popcount(bit)>=T){
						int tar=0;
						per(j,7)if(bit&1<<j){
							tar=tar*7+(7-fix[j]).v;
						}
						mint sum;
						for(auto [idxA,idxB]:lookup[bit][tar]){
							//mint mul=1;
							/*rep(j,6){
								int need=idx%7;
								idx/=7;
								int z=i/6+(j<i%6);
								if(j==0)z--;
								mul*=way[z][need];
							}*/
							//mul=wA[i][idx%343]*wB[i][idx/343];
							//ans+=parity(popcount(bit))*mul;
							//sum+=wA[i][idx%343]*wB[i][idx/343];
							sum+=wA[i][idxA]*wB[i][idxB];
						}
						ans+=parity(popcount(bit))*sum;
					}else if(popcount(bit)==1){
						int a=topbit(bit);
						int at=(-fix[a]).v;
						ans-=x[a][i][at];
					}else if(popcount(bit)==2){
						int a=botbit(bit);
						int at=(-fix[a]).v;
						int b=topbit(bit);
						int bt=(-fix[b]).v;
						ans+=y[a][b][i][at][bt];
					}else if(popcount(bit)==0){
						ans+=p2[i-1];
					}else{
						//assert(false);
					}
				}
			}
			
			add(i,-v);
		}
		add(i,mx);
		//cerr<<"Digit "<<i<<" Ans "<<ans<<endl;
	}
	add(0,-1);

	print(ans);
}

signed main(signed argc,char*argv[]){
	if(argc>1&&strcmp(argv[1],"D")==0)dbg=true;
	
	cin.tie(0);
	ios::sync_with_stdio(0);
	cout<<fixed<<setprecision(20);
	
	initp2();
	init();
	
	if(dbg){
		while(1){
			if(current_run_id%run_batch_size==0){
				cerr<<"Current Run "<<current_run_id<<endl;
			}
			slv();
			current_run_id++;
		}
	}else{
		int t;cin>>t;rep(_,t)
		slv();
	}
}