#include using namespace std; using ll = long long; using ld = long double; using ull = unsigned long long; using uint = unsigned int; using pcc = pair; using pii = pair; using pll = pair; using pdd = pair; using tuplis = array; template using pq = priority_queue, greater>; const ll LINF=0x1fffffffffffffff; const ll MINF=0x7fffffffffff; const int INF=0x3fffffff; const int MOD=1000000007; const int MODD=998244353; const ld DINF=numeric_limits::infinity(); const ld EPS=1e-9; const ld PI=3.1415926535897932; const ll four[] = {0, 1, 0, -1, 0}; const ll eight[] = {0, 1, 1, 0, -1, -1, 1, -1, 0}; #define overload4(_1,_2,_3,_4,name,...) name #define overload3(_1,_2,_3,name,...) name #define rep1(n) for(ll i=0;i=0;i--) #define rrep2(i,n) for(ll i=(n)-1;i>=0;i--) #define rrep3(i,a,b) for(ll i=(b)-1;i>=(a);i--) #define rrep4(i,a,b,c) for(ll i=a+(b-a-1)/c*c;i>=a;i-=c) #define rrep(...) overload4(__VA_ARGS__,rrep4,rrep3,rrep2,rrep1)(__VA_ARGS__) #define each(i,...) for(auto&& i:__VA_ARGS__) #define all1(i) begin(i),end(i) #define all2(i,a) begin(i),begin(i)+a #define all3(i,a,b) begin(i)+a,begin(i)+b #define all(...) overload3(__VA_ARGS__,all3,all2,all1)(__VA_ARGS__) #define rall1(i) (i).rbegin(),(i).rend() #define rall2(i,k) (i).rbegin(),(i).rbegin()+k #define rall3(i,a,b) (i).rbegin()+a,(i).rbegin()+b #define rall(...) overload3(__VA_ARGS__,rall3,rall2,rall1)(__VA_ARGS__) #define sum(...) accumulate(all(__VA_ARGS__),0LL) #define dsum(...) accumulate(all(__VA_ARGS__),0.0L) #define elif else if #define unless(a) if(!(a)) #define mp make_pair #define mt make_tuple #define INT(...) int __VA_ARGS__;in(__VA_ARGS__) #define LL(...) ll __VA_ARGS__;in(__VA_ARGS__) #define ULL(...) ull __VA_ARGS__;in(__VA_ARGS__) #define STR(...) string __VA_ARGS__;in(__VA_ARGS__) #define CHR(...) char __VA_ARGS__;in(__VA_ARGS__) #define DBL(...) double __VA_ARGS__;in(__VA_ARGS__) #define LD(...) ld __VA_ARGS__;in(__VA_ARGS__) #define Sort(a) sort(all(a)) #define Rev(a) reverse(all(a)) #define Uniq(a) sort(all(a));a.erase(unique(all(a)),end(a)) #define vec(type,name,...) vector name(__VA_ARGS__) #define VEC(type,name,size) vector name(size);in(name) #define vv(type,name,h,...) vector>name(h,vector(__VA_ARGS__)) #define VV(type,name,h,w) vector>name(h,vector(w));in(name) #define vvv(type,name,h,w,...) vector>>name(h,vector>(w,vector(__VA_ARGS__))) template auto max(const T& a){ return *max_element(all(a)); } template auto min(const T& a){ return *min_element(all(a)); } ll gcd(ll a, ll b){ while(b){ ll c = b; b = a % b; a = c; } return a; } ll lcm(ll a, ll b){ if(!a || !b) return 0; return a * b / gcd(a, b); } ll intpow(ll a, ll b){ ll ans = 1; while(b){ if(b & 1) ans *= a; a *= a; b /= 2; } return ans; } ll modpow(ll a, ll b, ll p){ ll ans = 1; while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; } template bool chmin(T& a, const T& b){ if(a > b){ a = b; return 1; } return 0; } template bool chmax(T& a, const T& b){ if(a < b){ a = b; return 1; } return 0; } vector factor(ull x){ vector ans; for(ll i = 2; i * i <= x; i++) if(x % i == 0){ ans.push_back({i, 1}); while((x /= i) % i == 0) ans.back().second++; } if(x != 1) ans.push_back({x, 1}); return ans; } vector divisor(ull x){ vector ans; for(ll i = 1; i * i <= x; i++) if(x % i == 0) ans.push_back(i); rrep(ans.size() - (ans.back() * ans.back() == x)) ans.push_back(x / ans[i]); return ans; } template unordered_map press(vector& a){ auto b = a; sort(all(b)); b.erase(unique(all(b)), b.end()); unordered_map ans; rep(b.size()) ans[b[i]] = i; each(i, a) i = ans[i]; return ans; } template map press_map(vector& a){ auto b = a; sort(all(b)); b.erase(unique(all(b)), b.end()); map ans; rep(b.size()) ans[b[i]] = i; each(i, a) i = ans[i]; return ans; } int scan(){ return getchar(); } void scan(int& a){ scanf("%d", &a); } void scan(unsigned& a){ scanf("%u", &a); } void scan(long& a){ scanf("%ld", &a); } void scan(long long& a){ scanf("%lld", &a); } void scan(unsigned long long& a){ scanf("%llu", &a); } void scan(char& a){ do{ a = getchar(); }while(a == ' ' || a == '\n'); } void scan(float& a){ scanf("%f", &a); } void scan(double& a){ scanf("%lf", &a); } void scan(long double& a){ scanf("%Lf", &a); } void scan(vector& a){ for(unsigned i = 0; i < a.size(); i++){ int b; scan(b); a[i] = b; } } void scan(char a[]){ scanf("%s", a); } void scan(string& a){ cin >> a; } template void scan(vector&); template void scan(array&); template void scan(pair&); template void scan(T(&)[size]); template void scan(vector& a){ for(auto&& i : a) scan(i); } template void scan(deque& a){ for(auto&& i : a) scan(i); } template void scan(array& a){ for(auto&& i : a) scan(i); } template void scan(pair& p){ scan(p.first); scan(p.second); } template void scan(T (&a)[size]){ for(auto&& i : a) scan(i); } template void scan(T& a){ cin >> a; } void in(){} template void in(Head& head, Tail&... tail){ scan(head); in(tail...); } void print(){ putchar(' '); } void print(bool a){ printf("%d", a); } void print(int a){ printf("%d", a); } void print(unsigned a){ printf("%u", a); } void print(long a){ printf("%ld", a); } void print(long long a){ printf("%lld", a); } void print(unsigned long long a){ printf("%llu", a); } void print(char a){ printf("%c", a); } void print(char a[]){ printf("%s", a); } void print(const char a[]){ printf("%s", a); } void print(float a){ printf("%.15f", a); } void print(double a){ printf("%.15f", a); } void print(long double a){ printf("%.15Lf", a); } void print(const string& a){ for(auto&& i : a) print(i); } template void print(const vector&); template void print(const array&); template void print(const pair& p); template void print(const T (&)[size]); template void print(const vector& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } } template void print(const deque& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } } template void print(const array& a){ print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } } template void print(const pair& p){ print(p.first); putchar(' '); print(p.second); } template void print(const T (&a)[size]){ print(a[0]); for(auto i = a; ++i != end(a); ){ putchar(' '); print(*i); } } template void print(const T& a){ cout << a; } int out(){ putchar('\n'); return 0; } template int out(const T& t){ print(t); putchar('\n'); return 0; } template int out(const Head& head, const Tail&... tail){ print(head); putchar(' '); out(tail...); return 0; } #ifdef DEBUG void err(){ putchar('\n'); } template void err(const T& t){ print(t); putchar('\n'); } template void err(const Head& head, const Tail&... tail){ print(head); putchar(' '); out(tail...); } #else template void err(const T&...){} #endif int first(bool i = true){ return out(i?"first":"second"); } int yes(bool i = true){ return out(i?"yes":"no"); } int Yes(bool i = true){ return out(i?"Yes":"No"); } int No(){ return out("No"); } int YES(bool i = true){ return out(i?"YES":"NO"); } int NO(){ return out("NO"); } int Yay(bool i = true){ return out(i?"Yay!":":("); } int possible(bool i = true){ return out(i?"possible":"impossible"); } int Possible(bool i = true){ return out(i?"Possible":"Impossible"); } int POSSIBLE(bool i = true){ return out(i?"POSSIBLE":"IMPOSSIBLE"); } void Case(ll i){ printf("Case #%lld: ", i); } namespace fft{ const int maxBase = 21; const int maxN = 1 << maxBase; struct num{ double x, y; num(){} num(double xx, double yy): x(xx), y(yy){} num(double alp): x(cos(alp)), y(sin(alp)){} }; inline static constexpr int pw(int a){ return 1 << a; } inline num operator+(num a, num b){ return num(a.x + b.x, a.y + b.y); } inline num operator-(num a, num b){ return num(a.x - b.x, a.y - b.y); } inline num operator*(num a, num b){ return num(a.x * b.x - a.y * b.y, a.x * b.y + a.y * b.x); } inline num conj(num a){ return num(a.x, -a.y); } const double PI = acos(-1); num root[maxN]; int rev[maxN]; bool rootsPrepared = false; void prepRoots(){ if(rootsPrepared) return; rootsPrepared = true; root[1] = num(1, 0); for(int k = 1; k < maxBase; ++k){ num x(2 * PI / pw(k + 1)); for(int i = pw(k - 1); i < pw(k); ++i){ root[2 * i] = root[i]; root[2 * i + 1] = root[i] * x; } } } int base, N; int lastRevN = -1; void prepRev(){ if(lastRevN == N) return; lastRevN = N; rep(i, N) rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (base - 1)); } void fft(num *a, num *f){ rep(i, N) f[i] = a[rev[i]]; for(int k = 1; k < N; k <<= 1) for(int i = 0; i < N; i += 2 * k) rep(j, k){ num z = f[i + j + k] * root[j + k]; f[i + j + k] = f[i + j] - z; f[i + j] = f[i + j] + z; } } num a[maxN], b[maxN], f[maxN], g[maxN]; ll A[maxN], B[maxN], C[maxN]; void _multMod(int mod){ rep(i, N){ int x = A[i] % mod; a[i] = num(x & (pw(15) - 1), x >> 15); } rep(i, N){ int x = B[i] % mod; b[i] = num(x & (pw(15) - 1), x >> 15); } fft(a, f); fft(b, g); rep(i, N){ int j = (N - i) & (N - 1); num a1 = (f[i] + conj(f[j])) * num(0.5, 0); num a2 = (f[i] - conj(f[j])) * num(0, -0.5); num b1 = (g[i] + conj(g[j])) * num(0.5 / N, 0); num b2 = (g[i] - conj(g[j])) * num(0, -0.5 / N); a[j] = a1 * b1 + a2 * b2 * num(0, 1); b[j] = a1 * b2 + a2 * b1; } fft(a, f); fft(b, g); rep(i, N){ ll aa = f[i].x + 0.5; ll bb = g[i].x + 0.5; ll cc = f[i].y + 0.5; C[i] = (aa + bb % mod * pw(15) + cc % mod * pw(30)) % mod; } } void prepAB(int n1, int n2){ base = 1; N = 2; while (N < n1 + n2) base++, N <<= 1; assert(base <= maxBase); for(int i = n1; i < N; ++i) A[i] = 0; for(int i = n2; i < N; ++i) B[i] = 0; prepRoots(); prepRev(); } void multMod(int n1, int n2, int mod){ prepAB(n1, n2); _multMod(mod); } } const int mod = MOD; struct FPS{ using vi = vector; vi v; FPS(){} FPS(const vi& vv){ v = vv; } int size() const { return static_cast(v.size()); } FPS cut(int maxLen){ if(maxLen < size()) v.resize(maxLen); return *this; } FPS norm(){ while (size() > 1 && v.back() == 0) v.pop_back(); return *this; } inline int& operator[](int i){ return v[i]; } inline const int& operator[](int i) const { return v[i]; } FPS operator+(const FPS& B) const { FPS C; C.v = vi(max(size(), B.size())); rep(i, C.size()){ if(i < size()){ C[i] += v[i]; if(C[i] >= mod) C[i] -= mod; } if(i < B.size()){ C[i] += B[i]; if(C[i] >= mod) C[i] -= mod; } } return C.norm(); } FPS operator-(const FPS& B) const { FPS C; C.v = vi(max(size(), B.size())); rep(i, C.size()){ if(i < size()){ C[i] += v[i]; if(C[i] >= mod) C[i] -= mod; } if(i < B.size()){ C[i] -= B[i]; if(C[i] < 0) C[i] += mod; } } return C.norm(); } FPS operator*(const FPS& B) const { FPS C; C.v = vi(size() + B.size() - 1); rep(i, size()) fft::A[i] = v.at(i); rep(i, B.size()) fft::B[i] = B[i]; fft::multMod(size(), B.size(), mod); rep(i, C.size()) C[i] = fft::C[i]; return C.norm(); } FPS _cutPoly(int l, int r) const { FPS R; R.v.resize(r - l); for(int i = l; i < r; ++i) if(i < size()) R[i - l] = v[i]; return R; }; int _rev(int x, int m) const { if(x == 1) return 1; return (1 - _rev(m % x, x) * (ll)m) / x + m; }; FPS inv(int n){ // returns A^-1 mod x^n assert(size() && v[0] != 0); cut(n); FPS R({_rev(v[0], mod)}); for(int k = 1; k < n; k <<= 1){ FPS A0 = _cutPoly(0, k); FPS A1 = _cutPoly(k, 2 * k); FPS H = A0 * R; H = H._cutPoly(k, 2 * k); FPS R1 = (((A1 * R).cut(k) + H) * (FPS({0}) - R)).cut(k); R.v.resize(2 * k); rep(i, k) R[i + k] = R1[i]; } return R.cut(n).norm(); } inline FPS rev() const { FPS f = *this; reverse(all(f.v)); return f; }; pair divide(FPS B, FPS &B1){ if(size() < B.size()) return {FPS({0}), *this}; FPS q = (B1*rev()).cut(size() - B.size() + 1).rev(); FPS r = *this - B * q; return {q, r}; } }; struct Modint{ uint num = 0; constexpr Modint(){} constexpr Modint(const Modint &x) : num(x.num){} inline constexpr operator ll() const { return num; } inline constexpr Modint& operator+=(Modint x){ num += x.num; if(num >= mod) num -= mod; return *this; } inline constexpr Modint& operator++(){ if(num == mod - 1) num = 0; else num++; return *this; } inline constexpr Modint operator++(int){ Modint ans(*this); operator++(); return ans; } inline constexpr Modint operator- () const { return Modint(0) -= *this; } inline constexpr Modint operator- (Modint x) const { return Modint(*this) -= x; } inline constexpr Modint& operator-=(Modint x){ if(num < x.num) num += mod; num -= x.num; return *this; } inline constexpr Modint& operator--(){ if(num == 0) num = mod - 1; else num--; return *this; } inline constexpr Modint operator--(int){ Modint ans(*this); operator--(); return ans; } inline constexpr Modint& operator*=(Modint x){ num = ull(num) * x.num % mod; return *this; } inline constexpr Modint& operator/=(Modint x){ return operator*=(x.inv()); } template constexpr Modint(T x){ using U = typename conditional= 4, T, int>::type; U y = x; y %= U(mod); if(y < 0) y += mod; num = uint(y); } template inline constexpr Modint operator+(T x) const { return Modint(*this) += x; } template inline constexpr Modint& operator+=(T x){ x %= mod; if(x < 0) x += mod; num += x; if(num >= mod) num -= mod; return *this; } template inline constexpr Modint operator- (T x) const { return Modint(*this) -= x; } template inline constexpr Modint& operator-=(T x){ return operator-=(Modint(x)); } template inline constexpr Modint operator* (T x) const { return Modint(*this) *= x; } template inline constexpr Modint& operator*=(T x){ return operator*=(Modint(x)); } template inline constexpr Modint operator/ (T x) const { return Modint(*this) /= x; } template inline constexpr Modint& operator/=(T x){ return operator/=(Modint(x)); } inline constexpr Modint inv() const { ll x = 0, y = 0; extgcd(num, mod, x, y); return x; } inline constexpr ll extgcd(ll a, ll b, ll &x, ll &y) const { ll g = a; x = 1; y = 0; if(b){ g = extgcd(b, a % b, y, x); y -= a / b * x; } return g; } inline constexpr Modint pow(ull x) const { Modint ans = 1, cnt = *this; while(x){ if(x & 1) ans *= cnt; cnt *= cnt; x /= 2; } return ans; } }; std::istream& operator>>(std::istream& is, Modint& x) { ll a; in(a); x = a; return is; } inline constexpr Modint operator""_M(ull x) { return Modint(x); } std::vector fac(1, 1), inv(1, 1); inline void reserve(ll a){ if(fac.size() >= a) return; if(a < fac.size() * 2) a = fac.size() * 2; if(a >= mod) a = mod; while(fac.size() < a) fac.push_back(fac.back() * Modint(fac.size())); inv.resize(fac.size()); inv.back() = fac.back().inv(); for(ll i = inv.size() - 1; !inv[i - 1]; i--) inv[i - 1] = inv[i] * i; } inline Modint fact(ll n){ if(n < 0) return 0; reserve(n + 1); return fac[n]; } inline Modint perm(ll n, ll r){ if(r < 0 || n < r) return 0; reserve(n + 1); return fac[n] * inv[n - r]; } inline Modint comb(ll n, ll r){ if(r < 0 || n < r) return 0; reserve(n + 1); return fac[n] * inv[r] * inv[n - r]; } inline Modint Mcomb(ll n, ll r){ return comb(n + r - 1, n - 1); } // r個をn部屋に分ける inline Modint catalan(ll n){ reserve(n * 2 + 1); return fac[n * 2] * inv[n] * inv[n + 1]; } signed main(){ LL(n,m,d1,d2); n--; vectora(m),b(m); rep(n+1){ ll at=(d2-d1+1)*i+d1*n; if(at