#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define rep(i,n) for(int (i)=0;(i)<(int)(n);++(i)) #define rer(i,l,u) for(int (i)=(int)(l);(i)<=(int)(u);++(i)) #define reu(i,l,u) for(int (i)=(int)(l);(i)<(int)(u);++(i)) #if defined(_MSC_VER) || __cplusplus > 199711L #define aut(r,v) auto r = (v) #else #define aut(r,v) __typeof(v) r = (v) #endif #define each(it,o) for(aut(it, (o).begin()); it != (o).end(); ++ it) #define all(o) (o).begin(), (o).end() #define pb(x) push_back(x) #define mp(x,y) make_pair((x),(y)) #define mset(m,v) memset(m,v,sizeof(m)) #define INF 0x3f3f3f3f #define INFL 0x3f3f3f3f3f3f3f3fLL using namespace std; typedef vector vi; typedef pair pii; typedef vector > vpii; typedef long long ll; template inline void amin(T &x, U y) { if(y < x) x = y; } template inline void amax(T &x, U y) { if(x < y) x = y; } template struct ModInt { static const int Mod = MOD; unsigned x; ModInt(): x(0) { } ModInt(signed sig) { int sigt = sig % MOD; if(sigt < 0) sigt += MOD; x = sigt; } ModInt(signed long long sig) { int sigt = sig % MOD; if(sigt < 0) sigt += MOD; x = sigt; } int get() const { return (int)x; } ModInt &operator+=(ModInt that) { if((x += that.x) >= MOD) x -= MOD; return *this; } ModInt &operator-=(ModInt that) { if((x += MOD - that.x) >= MOD) x -= MOD; return *this; } ModInt &operator*=(ModInt that) { x = (unsigned long long)x * that.x % MOD; return *this; } ModInt &operator/=(ModInt that) { return *this *= that.inverse(); } ModInt operator+(ModInt that) const { return ModInt(*this) += that; } ModInt operator-(ModInt that) const { return ModInt(*this) -= that; } ModInt operator*(ModInt that) const { return ModInt(*this) *= that; } ModInt operator/(ModInt that) const { return ModInt(*this) /= that; } ModInt inverse() const { signed a = x, b = MOD, u = 1, v = 0; while(b) { signed t = a / b; a -= t * b; std::swap(a, b); u -= t * v; std::swap(u, v); } if(u < 0) u += Mod; ModInt res; res.x = (unsigned)u; return res; } bool operator==(ModInt that) const { return x == that.x; } bool operator!=(ModInt that) const { return x != that.x; } ModInt operator-() const { ModInt t; t.x = x == 0 ? 0 : Mod - x; return t; } }; typedef ModInt<1000000007> mint; vector doDP(const int a[6], int n) { int maxX = a[5] * n; vector > dp(n+1, vector(maxX+1)); dp[0][0] = 1; rep(k, 6) { int t = a[k]; for(int i = n; i >= 0; -- i) { int maxx = k == 0 ? 0 : i * a[k-1]; rer(j, 0, maxx) { mint x = dp[i][j]; if(x.get() == 0) continue; rer(l, 1, n-i) dp[i+l][j + l * t] += x; } } } return dp[n]; } struct Polynomial { typedef mint Coef; typedef Coef Val; vector coef; //... + coef[2] x^2 + coef[1] x + coef[0] Polynomial() {} explicit Polynomial(int n): coef(n) {} static Polynomial One() { Polynomial r(1); r.coef[0] = 1; return r; } bool iszero() const { return coef.empty(); } int degree1() const { return coef.size(); } //degree + 1 int resize(int d) { if(degree1() < d) coef.resize(d); return d; } const Coef operator[](int i) const { return i >= degree1() ? Coef() : coef[i]; } void canonicalize() { int i = coef.size(); while(i > 0 && coef[i-1] == Coef()) i --; coef.resize(i); } Val evalute(Val x) const { int d = degree1(); Val t = 0, y = 1; rep(i, d) { t += y * coef[i]; y *= x; } return t; } Polynomial &operator+=(const Polynomial &that) { int d = resize(that.degree1()); for(int i = 0; i < d; i ++) coef[i] += that[i]; canonicalize(); return *this; } Polynomial operator+(const Polynomial &that) const { return Polynomial(*this) += that; } Polynomial &operator-=(const Polynomial &that) { int d = resize(that.degree1()); for(int i = 0; i < d; i ++) coef[i] -= that[i]; canonicalize(); return *this; } Polynomial operator-(const Polynomial &that) const { return Polynomial(*this) -= that; } Polynomial operator-() const { int d = degree1(); Polynomial res(d); for(int i = 0; i < d; i ++) res.coef[i] = - coef[i]; return res; } //naive Polynomial operator*(const Polynomial &that) const { if(iszero() || that.iszero()) return Polynomial(); int x = degree1(), y = that.degree1(), d = x + y - 1; Polynomial res(d); rep(i, x) rep(j, y) res.coef[i+j] += coef[i] * that.coef[j]; res.canonicalize(); return res; } //long division pair divmod(const Polynomial &that) const { int x = degree1() - 1, y = that.degree1() - 1; int d = max(0, x - y); Polynomial q(d + 1), r = *this; for(int i = x; i >= y; i --) { Coef t = r.coef[i] / that.coef[y]; q.coef[i - y] = t; assert(t * that.coef[y] == r.coef[i]); r.coef[i] = 0; for(int j = 0; j < y; j ++) r.coef[i - y + j] -= t * that.coef[j]; } q.canonicalize(); r.canonicalize(); return make_pair(q, r); } Polynomial operator/(const Polynomial &that) const { return divmod(that).first; } Polynomial operator%(const Polynomial &that) const { return divmod(that).second; } }; Polynomial powmod(Polynomial a, Polynomial m, unsigned long long k) { Polynomial r = Polynomial::One(); while(k) { if(k & 1) r = r * a % m; a = a * a % m; k >>= 1; } return r; } vector solveSmall(int N, const vector &ways) { vector dp(N+1); dp[0] = 1; int X = (int)ways.size() - 1; rep(i, N) { mint x = dp[i]; if(x.get() == 0) continue; rer(j, 1, X) dp[min(N, i + j)] += x * ways[j]; } return dp; } int main() { long long N; int P, C; while(~scanf("%lld%d%d", &N, &P, &C)) { const int primes[6] = { 2, 3, 5, 7, 11, 13 }; const int composites[6] = { 4, 6, 8, 9, 10, 12 }; vector cntP = doDP(primes, P); vector cntC = doDP(composites, C); int X = P * primes[5] + C * composites[5]; vector ways(X+1); rep(i, cntP.size()) rep(j, cntC.size()) ways[i + j] += cntP[i] * cntC[j]; // rer(i, 0, 100) // cerr << "ans " << i << " = " << solveSmall(i, ways)[i].get() << endl; if(N <= X * 2) { vector v = solveSmall((int)N, ways); mint ans = v[(int)N]; printf("%d\n", ans.get()); continue; } vector firstX = solveSmall(X, ways); Polynomial f(X+1); f.coef[X] = 1; rer(i, 1, X) f.coef[X - i] = -ways[i]; Polynomial x(2); x.coef[1] = 1; /* { Polynomial d = Polynomial::One(); rep(k, 30) { mint sum; rer(j, 0, X) sum += d[j] * firstX[j]; cerr << "a " << k << ": " << sum.get() << endl; d = d * x; d = d % f; } }*/ vector lastX(X); /* vector v = solveSmall(N + 2, ways); rep(i, X) lastX[i] = v[N - X + i]; */ // /* Polynomial d = powmod(x, f, N - X); rep(i, X) { mint sum; rer(j, 0, X) sum += d[j] * firstX[j]; lastX[i] = sum; // cerr << N - X + i << ": " << sum.get() << endl; d = d * x; d = d % f; } // */ mint ans; rep(i, X) { mint x = lastX[i]; rer(j, X - i, X) ans += x * ways[j]; } printf("%d\n", ans.get()); } return 0; }