#include using namespace std; #define rep(i,n) for(ll i=0;i=0;i--) #define perl(i,r,l) for(ll i=r-1;i>=l;i--) #define fi first #define se second #define ins insert #define pqueue(x) priority_queue,greater> #define all(x) (x).begin(),(x).end() #define CST(x) cout<; using vvl=vector>; using pl=pair; using vpl=vector; using vvpl=vector; const ll MOD=1000000007; const ll MOD9=998244353; const int inf=1e9+10; const ll INF=4e18; const ll dy[9]={1,0,-1,0,1,1,-1,-1,0}; const ll dx[9]={0,1,0,-1,1,-1,1,-1,0}; template inline bool chmax(T &a, T b) { return ((a < b) ? (a = b, true) : (false)); } template inline bool chmin(T &a, T b) { return ((a > b) ? (a = b, true) : (false)); } const int mod = MOD; const int max_n = 2000050; struct mint { ll x; // typedef long long ll; mint(ll x=0):x((x%mod+mod)%mod){} mint operator-() const { return mint(-x);} mint& operator+=(const mint a) { if ((x += a.x) >= mod) x -= mod; return *this; } mint& operator-=(const mint a) { if ((x += mod-a.x) >= mod) x -= mod; return *this; } mint& operator*=(const mint a) { (x *= a.x) %= mod; return *this;} mint operator+(const mint a) const { return mint(*this) += a;} mint operator-(const mint a) const { return mint(*this) -= a;} mint operator*(const mint a) const { return mint(*this) *= a;} mint pow(ll t) const { if (!t) return 1; mint a = pow(t>>1); a *= a; if (t&1) a *= *this; return a; } bool operator==(const mint &p) const { return x == p.x; } bool operator!=(const mint &p) const { return x != p.x; } // for prime mod mint inv() const { return pow(mod-2);} mint& operator/=(const mint a) { return *this *= a.inv();} mint operator/(const mint a) const { return mint(*this) /= a;} }; istream& operator>>(istream& is, mint& a) { return is >> a.x;} ostream& operator<<(ostream& os, const mint& a) { return os << a.x;} using vm=vector; using vvm=vector; struct combination { vector fact, ifact; combination(int n):fact(n+1),ifact(n+1) { assert(n < mod); fact[0] = 1; for (int i = 1; i <= n; ++i) fact[i] = fact[i-1]*i; ifact[n] = fact[n].inv(); for (int i = n; i >= 1; --i) ifact[i-1] = ifact[i]*i; } mint operator()(int n, int k) { if (k < 0 || k > n) return 0; return fact[n]*ifact[k]*ifact[n-k]; } }comb(max_n); namespace NTT { // int32型のmodが取れるFFT。auto c=NTT::mul(a,b,mod)で受け取り。TIME指定。 // ChineseRemと組み合わせてlong longにもできる std::vector tmp; size_t sz = 1; inline int powMod(int n, int p, int m) { int res = 1; while (p) { if (p & 1) res = (ll)res * n % m; n = (ll)n * n % m; p >>= 1; } return (int)res; } inline int invMod(int n, int m) { return powMod(n, m - 2, m); } template struct NTTPart { static std::vector ntt(std::vector a, bool inv = false) { size_t mask = sz - 1; size_t p = 0; for (size_t i = sz >> 1; i >= 1; i >>= 1) { auto& cur = (p & 1) ? tmp : a; auto& nex = (p & 1) ? a : tmp; int e = powMod(PrimitiveRoot, (Mod - 1) / sz * i, Mod); if (inv) e = invMod(e, Mod); int w = 1; for (size_t j = 0; j < sz; j += i) { for (size_t k = 0; k < i; ++k) { nex[j + k] = (cur[((j << 1) & mask) + k] + (ll)w * cur[(((j << 1) + i) & mask) + k]) % Mod; } w = (ll)w * e % Mod; } ++p; } if (p & 1) std::swap(a, tmp); if (inv) { int invSz = invMod(sz, Mod); for (size_t i = 0; i < sz; ++i) a[i] = (ll)a[i] * invSz % Mod; } return a; } static std::vector mul(std::vector a, std::vector b) { a = ntt(a); b = ntt(b); for (size_t i = 0; i < sz; ++i) a[i] = (ll)a[i] * b[i] % Mod; a = ntt(a, true); return a; } }; constexpr int M[] = {1224736769, 469762049, 167772161}; constexpr int PR[] = {3, 3, 3}; constexpr int NTT_CONVOLUTION_TIME = 3; /* X := max(a)*max(b)*max(|a|, |b|) のとき, NTT_CONVOLUTION_TIME <- 1: X < 1224736769 = 1.2*10^ 9 ~ 2^30 NTT_CONVOLUTION_TIME <- 2: X < 575334854091079681 = 5.8*10^17 ~ 2^59 NTT_CONVOLUTION_TIME <- 3: X < 2^86 (32bit * 32bit * 10^7くらいまで) */ inline void garner(std::vector *c, int mod) { if (NTT_CONVOLUTION_TIME == 1) { for(auto& x : c[0]) x %= mod; } else if (NTT_CONVOLUTION_TIME == 2) { const int r01 = invMod(M[0], M[1]); for (size_t i = 0; i < sz; ++i) { c[1][i] = (c[1][i] - c[0][i]) * (ll)r01 % M[1]; if (c[1][i] < 0) c[1][i] += M[1]; c[0][i] = (c[0][i] + (ll)c[1][i] * M[0]) % mod; } } else if (NTT_CONVOLUTION_TIME == 3) { const int R01 = invMod(M[0], M[1]); const int R02 = invMod(M[0], M[2]); const int R12 = invMod(M[1], M[2]); const int M01 = (ll)M[0] * M[1] % mod; for (size_t i = 0; i < sz; ++i) { c[1][i] = (c[1][i] - c[0][i]) * (ll)R01 % M[1]; if (c[1][i] < 0) c[1][i] += M[1]; c[2][i] = ((c[2][i] - c[0][i]) * (ll)R02 % M[2] - c[1][i]) * R12 % M[2]; if (c[2][i] < 0) c[2][i] += M[2]; c[0][i] = (c[0][i] + (ll)c[1][i] * M[0] + (ll)c[2][i] * M01) % mod; } } } std::vector mul(std::vector a, std::vector b, int mod) { for (auto& x : a) x %= mod; for (auto& x : b) x %= mod; size_t m = a.size() + b.size() - 1; sz = 1; while (m > sz) sz <<= 1; tmp.resize(sz); a.resize(sz, 0); b.resize(sz, 0); std::vector c[NTT_CONVOLUTION_TIME]; if (NTT_CONVOLUTION_TIME >= 1) c[0] = NTTPart::mul(a, b); if (NTT_CONVOLUTION_TIME >= 2) c[1] = NTTPart::mul(a, b); if (NTT_CONVOLUTION_TIME >= 3) c[2] = NTTPart::mul(a, b); for (auto& v : c) v.resize(m); garner(c, mod); return c[0]; } }; // !!! CHECK NTT_CONVOLUTION_TIME !!! int main(){ ll n,m;cin >> n >> m; ll x,y;cin >> x >> y; m-=x*(n-1);y-=x; if(m<=0){ cout << 0 << endl;return 0; } vector dp(m); ll cnt=0; for(ll i=0;i ndp(m); for(ll i=0;i sdp(m,1); //rep(i,m)cout << dp[i] <<" ";cout << endl; //rep(i,m)cout << ndp[i] <<" ";cout << endl; //rep(i,m)cout << sdp[i] <<" ";cout << endl; auto f=NTT::mul(dp,ndp,MOD); f=NTT::mul(f,sdp,MOD); mint ans=0; for(ll i=0;i