#line 1 "combined.cpp" #pragma region Macros #include using namespace std; template inline bool chmax(T &a, T b) { if(a < b) { a = b; return 1; } return 0; } template inline bool chmin(T &a, T b) { if(a > b) { a = b; return 1; } return 0; } #ifdef DEBUG template ostream &operator<<(ostream &os, const pair &p) { os << '(' << p.first << ',' << p.second << ')'; return os; } template ostream &operator<<(ostream &os, const vector &v) { os << '{'; for(int i = 0; i < (int)v.size(); i++) { if(i) { os << ','; } os << v[i]; } os << '}'; return os; } void debugg() { cerr << endl; } template void debugg(const T &x, const Args &... args) { cerr << " " << x; debugg(args...); } #define debug(...) \ cerr << __LINE__ << " [" << #__VA_ARGS__ << "]: ", debugg(__VA_ARGS__) #define dump(x) cerr << __LINE__ << " " << #x << " = " << (x) << endl #else #define debug(...) (void(0)) #define dump(x) (void(0)) #endif struct Setup { Setup() { cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } __Setup; using ll = long long; #define OVERLOAD3(_1, _2, _3, name, ...) name #define ALL(v) (v).begin(), (v).end() #define RALL(v) (v).rbegin(), (v).rend() #define REP1(i, n) for(int i = 0; i < int(n); i++) #define REP2(i, a, b) for(int i = (a); i < int(b); i++) #define REP(...) OVERLOAD3(__VA_ARGS__, REP2, REP1)(__VA_ARGS__) #define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end()) #define REVERSE(v) reverse(ALL(v)) #define SZ(v) ((int)(v).size()) const int INF = 1 << 30; const ll LLINF = 1LL << 60; constexpr int MOD = 1000000007; constexpr int MOD2 = 998244353; const int dx[4] = {1, 0, -1, 0}; const int dy[4] = {0, 1, 0, -1}; void Case(int i) { cout << "Case #" << i << ": "; } int popcount(int x) { return __builtin_popcount(x); } ll popcount(ll x) { return __builtin_popcountll(x); } #pragma endregion Macros #line 2 "/Users/siro53/kyo-pro/compro_library/modint/modint.hpp" #line 6 "/Users/siro53/kyo-pro/compro_library/modint/modint.hpp" template class ModInt { public: ModInt() : x(0) {} ModInt(long long y) : x(y >= 0 ? y % umod() : (umod() - (-y) % umod()) % umod()) {} unsigned int val() const { return x; } ModInt &operator+=(const ModInt &p) { if((x += p.x) >= umod()) x -= umod(); return *this; } ModInt &operator-=(const ModInt &p) { if((x += umod() - p.x) >= umod()) x -= umod(); return *this; } ModInt &operator*=(const ModInt &p) { x = (unsigned int)(1ULL * x * p.x % umod()); return *this; } ModInt &operator/=(const ModInt &p) { *this *= p.inv(); return *this; } ModInt operator-() const { return ModInt(-(long long)x); } ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; } ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; } ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; } ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; } bool operator==(const ModInt &p) const { return x == p.x; } bool operator!=(const ModInt &p) const { return x != p.x; } ModInt inv() const { long long a = x, b = mod, u = 1, v = 0, t; while(b > 0) { t = a / b; std::swap(a -= t * b, b); std::swap(u -= t * v, v); } return ModInt(u); } ModInt pow(unsigned long long n) const { ModInt ret(1), mul(x); while(n > 0) { if(n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } friend std::ostream &operator<<(std::ostream &os, const ModInt &p) { return os << p.x; } friend std::istream &operator>>(std::istream &is, ModInt &a) { long long t; is >> t; a = ModInt(t); return (is); } static constexpr int get_mod() { return mod; } private: unsigned int x; static constexpr unsigned int umod() { return mod; } }; #line 78 "combined.cpp" using mint = ModInt; #line 2 "/Users/siro53/kyo-pro/compro_library/math/binom.hpp" #line 6 "/Users/siro53/kyo-pro/compro_library/math/binom.hpp" template class Binomial { public: explicit Binomial(): Binomial(1) {} explicit Binomial(int MAX) : f(MAX, mint(1)), f_inv(MAX, mint(1)) { for(int i = 1; i < MAX; i++) f[i] = f[i-1] * mint(i); f_inv[MAX - 1] = f[MAX - 1].inv(); for(int i = MAX - 2; i >= 1; i--) { f_inv[i] = f_inv[i + 1] * mint(i + 1); } } void extend() { int n = (int)f.size(); f.resize(n * 2); f_inv.resize(n * 2); for(int i = n; i < n * 2; i++) f[i] = f[i - 1] * mint(i); f_inv[n * 2 - 1] = f[n * 2 - 1].inv(); for(int i = n * 2 - 2; i >= n; i--) { f_inv[i] = f_inv[i + 1] * mint(i + 1); } } mint fac(int n) { if(n < 0) return mint(0); while(n >= (int)f.size()) extend(); return f[n]; } mint fac_inv(int n) { if(n < 0) return mint(0); while(n >= (int)f_inv.size()) extend(); return f_inv[n]; } mint inv(int n) { if(n < 0) return -mint(-n); assert(n != 0); while(n >= (int)f_inv.size()) extend(); return (f_inv[n] * f[n - 1]); } mint binom(int n, int k) { if(n < k || n < 0 || k < 0) return mint(0); return (fac(n) * fac_inv(k) * fac_inv(n - k)); } mint binom_naive(long long n, long long k) { if(n < k || n < 0 || k < 0) return mint(0); mint res(1); k = std::min(k, n - k); for(int i = 0; i < k; i++) res *= inv(i + 1) * mint(n - i); return res; } mint perm(int n, int k) { if(n < k || n < 0 || k < 0) return mint(0); return (fac(n) * fac_inv(n - k)); } mint hom(int n, int k) { if(n < 0 || k < 0) return mint(0); return (k == 0 ? mint(1) : binom(n + k - 1, k)); } private: std::vector f, f_inv; }; #line 2 "/Users/siro53/kyo-pro/compro_library/math/divisor.hpp" #line 5 "/Users/siro53/kyo-pro/compro_library/math/divisor.hpp" template std::vector divisor(T n) { static_assert(std::is_integral::value == true, "type 'T' should be integer."); std::vector ret; for(T i = 1; i * i <= n; i++) { if(n % i == 0) { ret.push_back(i); if(i * i != n) ret.push_back(n / i); } } std::sort(ret.begin(), ret.end()); return ret; } #line 81 "combined.cpp" int main() { ll N, M; cin >> N >> M; Binomial comb; auto calc = [&](ll a, ll b) -> mint { if((a + b + N) % 2) return 0; ll j = (a + b + N) / 2; ll i = j - b; if(i < 0 or i > N or j < 0 or j > N) return 0; debug(a, b, i, j); return comb.binom(N, i) * comb.binom(N, j); }; mint ans = 0; if(M == 0) { REP(a, -N, N+1) ans += calc(a, a); ans *= mint(4).inv().pow(N); cout << ans << endl; return 0; } auto divs = divisor(abs(M)); for(ll d1 : divs) { ll d2 = M / d1; if(M > 0) { if((d1 + d2) % 2 == 0) { ll a = (d1 + d2) / 2; ll b = d1 - a; ans += calc(a, b); } if(abs(- d1 - d2) % 2 == 0) { ll a = (- d1 - d2) / 2; ll b = - d1 - a; ans += calc(a, b); } } else { if(abs(-d1 + d2) % 2 == 0) { ll a = (-d1 + d2) / 2; ll b = -d1 - a; ans += calc(a, b); } if(abs(d1 - d2) % 2 == 0) { ll a = (d1 - d2) / 2; ll b = d1 - a; ans += calc(a, b); } } } ans *= mint(4).inv().pow(N); cout << ans << endl; }