#define INF 4'000'000'000'000'000'037LL #include using namespace std; namespace { using ll = long long; using uint = unsigned int; using ull = unsigned long long; using pll = pair; #define vc vector template using vvc = vc>; using vpll = vc; #ifdef __SIZEOF_INT128__ using i128 = __int128_t; using u128 = __uint128_t; #endif #define cauto const auto #define overload4(_1, _2, _3, _4, name, ...) name #define rep1(i, n) for (ll i = 0, nnnnn = ll(n); i < nnnnn; i++) #define rep(...) overload4(__VA_ARGS__, rep3, rep2, rep1)(__VA_ARGS__) #define repi1(i, n) for (int i = 0, nnnnn = int(n); i < nnnnn; i++) #define repi(...) overload4(__VA_ARGS__, repi3, repi2, repi1)(__VA_ARGS__) template inline bool chmin(T &a, U b) { return a > b ? a = b, true : false; } template inline constexpr T divfloor(U a, V b) { return T(a) / T(b) - (T(a) % T(b) && (T(a) ^ T(b)) < 0); } template inline constexpr T safemod(U a, V b) { return T(a) - T(b) * divfloor(a, b); } template constexpr T ipow(U a, V b) { assert(b >= 0); if (b == 0) return 1; if (a == 0 || a == 1) return a; if (a < 0 && a == -1) return b & 1 ? -1 : 1; T res = 1, tmp = a; while (true) { if (b & 1) res *= tmp; b >>= 1; if (b == 0) break; tmp *= tmp; } return res; } template T mul_limited(A a, B b, M m) { assert(a >= 0 && b >= 0 && m >= 0); if (b == 0) return 0; return T(a) > T(m) / T(b) ? T(m) : T(a) * T(b); } template T mul_limited(A a, B b) { return mul_limited(a, b, INF); } template T pow_limited(A a, B b, M m) { assert(a >= 0 && b >= 0 && m >= 0); if (a <= 1 || b == 0) return min(ipow(a, b), T(m)); T res = 1, tmp = a; while (true) { if (b & 1) { if (res > T(m) / tmp) return m; res *= tmp; } b >>= 1; if (b == 0) break; if (tmp > T(m) / tmp) return m; tmp *= tmp; } return res; } template T pow_limited(A a, B b) { return pow_limited(a, b, INF); } #define ALL(a) (a).begin(), (a).end() template auto dvec(const V (&sz)[d], const T &init) { if constexpr (i < d) return vc(sz[i], dvec(sz, init)); else return init; } #if __cplusplus < 202002L #else #endif template void unique(V &v) { v.erase(std::unique(ALL(v)), v.end()); } template void rotate(V &v, U k) { const U n = v.size(); k = (k % n + n) % n; std::rotate(v.begin(), v.begin() + k, v.end()); } const vpll DRULgrid = {{1, 0}, {0, 1}, {-1, 0}, {0, -1}}; const vpll DRULplane = {{0, -1}, {1, 0}, {0, 1}, {-1, 0}}; template struct is_random_access_iterator { static constexpr bool value = is_same_v< typename iterator_traits::iterator_category, random_access_iterator_tag >; }; template constexpr bool is_random_access_iterator_v = is_random_access_iterator::value; #if __cplusplus < 202002L namespace internal { }; #else #endif #if __cplusplus < 202002L #else inline constexpr ll bit_width(ll x) { return std::bit_width((ull)x); } inline constexpr ll bit_floor(ll x) { return std::bit_floor((ull)x); } inline constexpr ll bit_ceil(ll x) { return std::bit_ceil((ull)x); } inline constexpr ll countr_zero(ll x) { assert(x != 0); return std::countr_zero((ull)x); } inline constexpr ll popcount(ll x) { return std::popcount((ull)x); } inline constexpr bool has_single_bit(ll x) { return std::has_single_bit((ull)x); } #endif #define dump(...) #define oj(...) __VA_ARGS__ namespace fastio { static constexpr uint32_t SIZ = 1 << 17; char ibuf[SIZ]; char obuf[SIZ]; char out[100]; uint32_t pil = 0, pir = 0, por = 0; struct Pre { char num[10000][4]; constexpr Pre() : num() { for (int i = 0; i < 10000; i++) { int n = i; for (int j = 3; j >= 0; j--) { num[i][j] = n % 10 | '0'; n /= 10; } } } } constexpr pre; inline void load() { memcpy(ibuf, ibuf + pil, pir - pil); pir = pir - pil + fread(ibuf + pir - pil, 1, SIZ - pir + pil, stdin); pil = 0; if (pir < SIZ) ibuf[pir++] = '\n'; } inline void flush() { fwrite(obuf, 1, por, stdout); por = 0; } template void rd1_integer(T &x) { if (pil + 100 > pir) load(); char c; do c = ibuf[pil++]; while (c < '-'); bool minus = 0; if constexpr (is_signed::value || is_same_v) { if (c == '-') { minus = 1, c = ibuf[pil++]; } } x = 0; while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; } if constexpr (is_signed::value || is_same_v) { if (minus) x = -x; } } void rd1(ll &x) { rd1_integer(x); } template void rd1(pair &p) { return rd1(p.first), rd1(p.second); } template void rd1_tuple(T &t) { if constexpr (N < std::tuple_size::value) { auto &x = std::get(t); rd1(x); rd1_tuple(t); } } template void rd1(tuple &tpl) { rd1_tuple(tpl); } template void rd1(array &x) { for (auto &d: x) rd1(d); } template void rd1(vc &x) { for (auto &d: x) rd1(d); } void read() {} template void read(H &h, T &... t) { rd1(h), read(t...); } void wt1(const char c) { if (por == SIZ) flush(); obuf[por++] = c; } template void wt1_integer(T x) { if (por > SIZ - 100) flush(); if (x < 0) { obuf[por++] = '-', x = -x; } int outi; for (outi = 96; x >= 10000; outi -= 4) { memcpy(out + outi, pre.num[x % 10000], 4); x /= 10000; } if (x >= 1000) { memcpy(obuf + por, pre.num[x], 4); por += 4; } else if (x >= 100) { memcpy(obuf + por, pre.num[x] + 1, 3); por += 3; } else if (x >= 10) { int q = (x * 103) >> 10; obuf[por] = q | '0'; obuf[por + 1] = (x - q * 10) | '0'; por += 2; } else obuf[por++] = x | '0'; memcpy(obuf + por, out + outi + 4, 96 - outi); por += 96 - outi; } template , int> = 0> void wt1(T x) { wt1_integer(x); } template void wt1(const pair &val) { wt1(val.first); wt1(' '); wt1(val.second); } template void wt1_tuple(const T &t) { if constexpr (N < std::tuple_size::value) { if constexpr (N > 0) { wt1(' '); } const auto x = std::get(t); wt1(x); wt1_tuple(t); } } template void wt1(const tuple &tpl) { wt1_tuple(tpl); } template void wt1(const array &val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) wt1(' '); wt1(val[i]); } } template void wt1(const vector &val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) wt1(' '); wt1(val[i]); } } void print() { wt1('\n'); } template void print(Head &&head, Tail &&... tail) { wt1(head); if (sizeof...(Tail)) wt1(' '); print(forward(tail)...); } } // namespace fastio struct Dummy { Dummy() { atexit(fastio::flush); } } dummy; namespace internal { template void READnodump(Ts &...a) { fastio::read(a...); } template void READVECnodump(int n, vc &v) { v.resize(n); READnodump(v); } template void READVECnodump(int n, vc &v, vc &...vs) { READVECnodump(n, v), READVECnodump(n, vs...); } template void READVEC2nodump(int n, int m, vvc &v) { v.assign(n, vc(m)); READnodump(v); } template void READVEC2nodump(int n, int m, vvc &v, vvc &...vs) { READVEC2nodump(n, m, v), READVEC2nodump(n, m, vs...); } template void READJAGnodump(int n, vvc &v) { v.resize(n); repi(i, n) { int k; READnodump(k); READVECnodump(k, v[i]); } } template void READJAGnodump(int n, vvc &v, vvc &...vs) { READJAGnodump(n, v), READJAGnodump(n, vs...); } }; // namespace internal #define READ(...) internal::READnodump(__VA_ARGS__); dump(__VA_ARGS__) #define IN(T, ...) T __VA_ARGS__; READ(__VA_ARGS__) #define LL(...) IN(ll, __VA_ARGS__) #define PRINT fastio::print template pair operator+=(pair &a, const P &b) { a.first += b.first; a.second += b.second; return a; } template pair operator+(pair &a, const P &b) { return a += b; } template array operator+=(array &a, const A &b) { for (size_t i = 0; i < n; i++) a[i] += b[i]; return a; } template array operator+(array &a, const A &b) { return a += b; } namespace internal { template auto tuple_add_impl(A &a, const B &b, const index_sequence) { ((get(a) += get(b)), ...); return a; } }; // namespace internal template tuple operator+=(tuple &a, const Tp &b) { return internal::tuple_add_impl(a, b, make_index_sequence>>{}); } template tuple operator+(tuple &a, const Tp &b) { return a += b; } namespace internal { }; mt19937_64 mt; namespace internal { constexpr ll powmod32_constexpr(ll x, ll n, int m) { if (m == 1) return 0; uint _m = (uint)m; ull r = 1; ull y = safemod(x, m); while (n) { if (n & 1) r = (r * y) % _m; y = (y * y) % _m; n >>= 1; } return r; } constexpr bool isprime32_constexpr(int n) { if (n <= 1) return false; if (n == 2 || n == 7 || n == 61) return true; if (n % 2 == 0) return false; ll d = n - 1; while (d % 2 == 0) d /= 2; constexpr ll bases[3] = {2, 7, 61}; for (ll a : bases) { ll t = d; ll y = powmod32_constexpr(a, t, n); while (t != n - 1 && y != 1 && y != n - 1) { y = y * y % n; t <<= 1; } if (y != n - 1 && t % 2 == 0) return false; } return true; } template constexpr bool isprime32 = isprime32_constexpr(n); struct barrett32 { uint m; ull im; explicit barrett32(uint m) : m(m), im((ull)(-1) / m + 1) {} uint umod() const { return m; } uint mul(uint a, uint b) const { ull z = a; z *= b; ull x = (ull)((u128(z)*im) >> 64); ull y = x * m; return (uint)(z - y + (z < y ? m : 0)); } }; } namespace internal { #define REF static_cast(*this) #define CREF static_cast(*this) #define VAL *static_cast(this) template struct modint_base { mint &operator+=(const mint &rhs) { mint &self = REF; self._v += rhs._v; if (self._v >= self.umod()) self._v -= self.umod(); return self; } mint &operator-=(const mint &rhs) { mint &self = REF; self._v -= rhs._v; if (self._v >= self.umod()) self._v += self.umod(); return self; } mint &operator/=(const mint &rhs) { mint &self = REF; return self = self * rhs.inv(); } mint &operator++() { mint &self = REF; self._v++; if (self._v == self.umod()) self._v = 0; return self; } mint &operator--() { mint &self = REF; if (self._v == 0) self._v = self.umod(); self._v--; return self; } mint operator++(int) { mint res = VAL; ++REF; return res; } mint operator--(int) { mint res = VAL; --REF; return res; } mint operator+() const { return VAL; } mint operator-() const { return mint() - VAL; } mint pow(ll n) const { assert(n >= 0); mint x = VAL, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } friend mint operator+(const mint &lhs, const mint &rhs) { return mint(lhs) += rhs; } friend mint operator-(const mint &lhs, const mint &rhs) { return mint(lhs) -= rhs; } friend mint operator*(const mint &lhs, const mint &rhs) { return mint(lhs) *= rhs; } friend mint operator/(const mint &lhs, const mint &rhs) { return mint(lhs) /= rhs; } friend bool operator==(const mint &lhs, const mint &rhs) { return mint(lhs).eq(rhs); } friend bool operator!=(const mint &lhs, const mint &rhs) { return mint(lhs).neq(rhs); } private: bool eq(const mint &rhs) { return REF._v == rhs._v; } bool neq(const mint &rhs) { return REF._v != rhs._v; } }; } template , T>, int> = 0> void rd1(T &x) { ll a; fastio::rd1(a); x = a; } template , T>, int> = 0> void wt1(const T &x) { fastio::wt1(x.val()); } template constexpr tuple extgcd(const T &a, const T &b) { if (a == 0 && b == 0) return {0, 0, 0}; T x1 = 1, y1 = 0, z1 = a; T x2 = 0, y2 = 1, z2 = b; while (z2 != 0) { T q = z1 / z2; tie(x1, x2) = make_pair(x2, x1 - q * x2); tie(y1, y2) = make_pair(y2, y1 - q * y2); tie(z1, z2) = make_pair(z2, z1 - q * z2); } if (z1 < 0) x1 = -x1, y1 = -y1, z1 = -z1; return {z1, x1, y1}; } template struct static_modint : internal::modint_base> { using mint = static_modint; private: friend struct internal::modint_base>; uint _v; static constexpr uint umod() { return m; } static constexpr bool prime = internal::isprime32; public: static constexpr int mod() { return m; } static mint raw(int v) { mint x; x._v = v; return x; } static_modint() : _v(0) {} template static_modint(T v) { if constexpr (is_signed_v) { ll x = (ll)(v % (ll)(umod())); if (x < 0) x += umod(); _v = (uint)x; } else if constexpr (is_unsigned_v) { _v = (uint)(v % umod()); } else { static_assert(is_signed_v || is_unsigned_v, "Unsupported Type"); } } int val() const { return (int)_v; } mint& operator*=(const mint &rhs) { ull z = _v; z *= rhs._v; _v = (uint)(z % umod()); return *this; } mint inv() const { if (prime) { assert(_v != 0); return CREF.pow(umod() - 2); } else { auto [g, x, y] = extgcd(_v, m); assert(g == 1); return x; } } }; template struct dynamic_modint : internal::modint_base> { using mint = dynamic_modint; private: friend struct internal::modint_base>; uint _v; static internal::barrett32 bt; static uint umod() { return bt.umod(); } public: static int mod() { return (int)(bt.umod()); } static mint raw(int v) { mint x; x._v = v; return x; } dynamic_modint() : _v(0) {} template dynamic_modint(T v) { if constexpr (is_signed_v) { ll x = (ll)(v % (ll)(umod())); if (x < 0) x += umod(); _v = (uint)x; } else if constexpr (is_unsigned_v) { _v = (uint)(v % umod()); } else { static_assert(is_signed_v || is_unsigned_v, "Unsupported Type"); } } int val() const { return (int)_v; } mint& operator*=(const mint &rhs) { _v = bt.mul(_v, rhs._v); return *this; } mint inv() const { auto [g, x, y] = extgcd(_v, mod()); assert(g == 1); return x; } }; template internal::barrett32 dynamic_modint::bt(998244353); using modint1000000007 = static_modint<1000000007>; template struct is_static_modint : false_type {}; template struct is_static_modint> : true_type {}; template inline constexpr bool is_static_modint_v = is_static_modint::value; template struct is_dynamic_modint : false_type {}; template struct is_dynamic_modint> : true_type {}; template inline constexpr bool is_dynamic_modint_v = is_dynamic_modint::value; template struct PowerTable { private: decltype(T::mod()) mod; T base; vc pw; public: PowerTable() {} PowerTable(T base) : mod(T::mod()), base(base), pw(1, 1) {} void reserve(int n) { if (mod != T::mod()) { mod = T::mod(); pw = {1}; } int i = pw.size(); if (n < i) return; pw.resize(n + 1); for (; i <= n; i++) pw[i] = pw[i - 1] * base; } T pow(int n) { reserve(n); return pw[n]; } }; template struct Binomial { private: static decltype(T::mod()) mod; static vc fac_, finv_, inv_; public: static void reserve(int n) { if (mod != T::mod()) { mod = T::mod(); fac_ = {1, 1}, finv_ = {1, 1}, inv_ = {0, 1}; } int i = fac_.size(); chmin(n, T::mod() - 1); if (n < i) return; fac_.resize(n + 1), finv_.resize(n + 1), inv_.resize(n + 1); for (; i <= n; i++) { fac_[i] = fac_[i - 1] * T::raw(i); inv_[i] = -inv_[T::mod() % i] * T::raw(T::mod() / i); finv_[i] = finv_[i - 1] * inv_[i]; } } static T inv(T n) { assert(n != 0); reserve(n.val()); return inv_[n.val()]; } static T C(int n, int k) { if (n < k) return 0; if (n < 0 || k < 0) return 0; reserve(n); return fac_[n] * finv_[k] * finv_[n - k]; } static T H(int n, int k) { if (n == 0 && k == 0) return 1; return C(n + k - 1, k); } }; template decltype(T::mod()) Binomial::mod{}; template vc Binomial::fac_{}; template vc Binomial::finv_{}; template vc Binomial::inv_{}; using mint = modint1000000007; using bi = Binomial; template struct GroupAddSub { using S = T; static constexpr S op(S a, S b) { return a + b; } static constexpr S e() { return S(0); } static constexpr S inv(S a) { return -a; } }; template > struct CumulativeSum { using S = typename G::S; private: vc s; public: CumulativeSum() {} CumulativeSum(const vc &a) { const int n = a.size(); s.resize(n + 1, G::e()); repi(i, n) s[i + 1] = G::op(s[i], a[i]); } }; template > struct Imos { using S = typename G::S; private: vc d; public: Imos() {} Imos(int n) : d(n, G::e()) {} Imos(const vc &a) { const int n = a.size(); d.assign(n, G::e()); repi(i, n) add(i, i + 1, a[i]); } void add(int l, int r, const S &v) { const int n = d.size(); assert(0 <= l && l <= r && r <= n); d[l] = G::op(d[l], v); if (r != n) d[r] = G::op(d[r], G::inv(v)); } }; void init() { oj(mt.seed(random_device()())); } void main2() { LL(N, M, L, R); mint ans = 0; rep(i, M) { ll j = M - 1 - i; if ((j - L * (N - 1)) % (R - L + 1) != 0) continue; ll v = (j - L * (N - 1)) / (R - L + 1); if (v < 0) continue; mint x = bi::H(N + 1, i); mint y = ipow(-1, v) * bi::C(N - 1, v); ans += x * y; } PRINT(ans); } void test() { } template struct Main { Main() { cauto CERR = [](string val, string color) { string s = "\033[" + color + "m" + val + "\033[m"; /* コードテストで確認する際にコメントアウトを外す cerr << val; //*/ }; CERR("\n[FAST_IO]\n\n", "32"); cout << fixed << setprecision(20); test(); init(); CERR("\n[SINGLE_TESTCASE]\n\n", "36"); main2(); } }; Main main_dummy; } int main() {}