#pragma GCC optimize("O3") #pragma GCC optimize(2) #pragma GCC optimize(3) #pragma GCC optimize("Ofast") #pragma GCC optimize("inline") #pragma GCC optimize("-fgcse") #pragma GCC optimize("-fgcse-lm") #pragma GCC optimize("-fipa-sra") #pragma GCC optimize("-ftree-pre") #pragma GCC optimize("-ftree-vrp") #pragma GCC optimize("-fpeephole2") #pragma GCC optimize("-ffast-math") #pragma GCC optimize("-fsched-spec") #pragma GCC optimize("unroll-loops") #pragma GCC optimize("-falign-jumps") #pragma GCC optimize("-falign-loops") #pragma GCC optimize("-falign-labels") #pragma GCC optimize("-fdevirtualize") #pragma GCC optimize("-fcaller-saves") #pragma GCC optimize("-fcrossjumping") #pragma GCC optimize("-fthread-jumps") #pragma GCC optimize("-funroll-loops") #pragma GCC optimize("-freorder-blocks") #pragma GCC optimize("-fschedule-insns") #pragma GCC optimize("inline-functions") #pragma GCC optimize("-ftree-tail-merge") #pragma GCC optimize("-fschedule-insns2") #pragma GCC optimize("-fstrict-aliasing") #pragma GCC optimize("-falign-functions") #pragma GCC optimize("-fcse-follow-jumps") #pragma GCC optimize("-fsched-interblock") #pragma GCC optimize("-fpartial-inlining") #pragma GCC optimize("no-stack-protector") #pragma GCC optimize("-freorder-functions") #pragma GCC optimize("-findirect-inlining") #pragma GCC optimize("-fhoist-adjacent-loads") #pragma GCC optimize("-frerun-cse-after-loop") #pragma GCC optimize("inline-small-functions") #pragma GCC optimize("-finline-small-functions") #pragma GCC optimize("-ftree-switch-conversion") #pragma GCC optimize("-foptimize-sibling-calls") #pragma GCC optimize("-fexpensive-optimizations") #pragma GCC optimize("inline-functions-called-once") #pragma GCC optimize("-fdelete-null-pointer-checks") #pragma GCC optimize("Ofast") #include using namespace std; using ll = long long; template struct MINT{ int v; MINT() : v(0) {} MINT(ll val){ v = (-M <= val && val < M) ? val : val % M; if(v < 0) v += M; } friend istream& operator >> (istream &is, MINT &a) { ll t; is >> t; a = MINT(t); return is; } friend ostream& operator << (ostream &os, const MINT &a) { return os << a.v; } friend bool operator == (const MINT &a, const MINT &b) { return a.v == b.v; } friend bool operator != (const MINT &a, const MINT &b) { return a.v != b.v; } friend MINT pw(MINT a, ll b){ MINT ret= 1; while(b){ if(b & 1) ret *= a; b >>= 1; a *= a; } return ret; } friend MINT inv(const MINT a) { return pw(a, M-2); } MINT operator - () const { return MINT(-v); } MINT& operator += (const MINT m) { if((v += m.v) >= M) v -= M; return *this; } MINT& operator -= (const MINT m) { if((v -= m.v) < 0) v += M; return *this; } MINT& operator *= (const MINT m) { v = (ll)v*m.v%M; return *this; } MINT& operator /= (const MINT m) { *this *= inv(m); return *this; } friend MINT operator + (MINT a, MINT b) { a += b; return a; } friend MINT operator - (MINT a, MINT b) { a -= b; return a; } friend MINT operator * (MINT a, MINT b) { a *= b; return a; } friend MINT operator / (MINT a, MINT b) { a /= b; return a; } operator int32_t() const { return v; } operator int64_t() const { return v; } }; namespace fft{ template static void NTT(vector> &f, bool inv_fft = false){ using T = MINT; int N = f.size(); vector root(N >> 1); for(int i=1, j=0; i> 1; while(j >= bit) j -= bit, bit >>= 1; j += bit; if(i < j) swap(f[i], f[j]); } T ang = pw(T(W), (M-1)/N); if(inv_fft) ang = inv(ang); root[0] = 1; for(int i=1; i>1; i++) root[i] = root[i-1] * ang; for(int i=2; i<=N; i<<=1){ int step = N / i; for(int j=0; j>1)] * root[k*step]; f[j+k] = u + v; f[j+k+(i>>1)] = u - v; } } } if(inv_fft){ T rev = inv(T(N)); for(int i=0; i vector> multiply_ntt(vector> a, vector> b){ int N = 2; while(N < a.size() + b.size()) N <<= 1; a.resize(N); b.resize(N); NTT(a); NTT(b); for(int i=0; i(a, true); return a; } } template struct PolyMod{ using T = MINT; vector a; // constructor PolyMod(){} PolyMod(T a0) : a(1, a0) { normalize(); } PolyMod(const vector a) : a(a) { normalize(); } // method from vector int size() const { return a.size(); } int deg() const { return a.size() - 1; } void normalize(){ while(a.size() && a.back() == T(0)) a.pop_back(); } T operator [] (int idx) const { return a[idx]; } typename vector::const_iterator begin() const { return a.begin(); } typename vector::const_iterator end() const { return a.end(); } void push_back(const T val) { a.push_back(val); } void pop_back() { a.pop_back(); } // basic manipulation PolyMod reversed() const { vector b = a; reverse(b.begin(), b.end()); return b; } PolyMod trim(int n) const { return vector(a.begin(), a.begin() + min(n, size())); } PolyMod inv(int n){ PolyMod q(T(1) / a[0]); for(int i=1; i(a, b.a); normalize(); return *this; } PolyMod operator /= (const PolyMod &b){ if(deg() < b.deg()) return *this = PolyMod(); int sz = deg() - b.deg() + 1; PolyMod ra = reversed().trim(sz), rb = b.reversed().trim(sz).inv(sz); *this = (ra * rb).trim(sz); for(int i=sz-size(); i; i--) push_back(T(0)); reverse(a.begin(),a.end()); normalize(); return *this; } PolyMod operator %= (const PolyMod &b){ if(deg() < b.deg()) return *this; PolyMod tmp = *this; tmp /= b; tmp *= b; *this -= tmp; normalize(); return *this; } // operator PolyMod operator * (const T x) const { return PolyMod(*this) *= x; } PolyMod operator / (const T x) const { return PolyMod(*this) /= x; } PolyMod operator + (const PolyMod &b) const { return PolyMod(*this) += b; } PolyMod operator - (const PolyMod &b) const { return PolyMod(*this) -= b; } PolyMod operator * (const PolyMod &b) const { return PolyMod(*this) *= b; } PolyMod operator / (const PolyMod &b) const { return PolyMod(*this) /= b; } PolyMod operator % (const PolyMod &b) const { return PolyMod(*this) %= b; } }; constexpr int W = 3, MOD = 1e9 + 7; using mint = MINT; using poly = PolyMod; mint kitamasa(poly c, poly a, ll n){ poly d = vector{1}; poly xn = vector{0, 1}; poly f; for(int i=0; i>= 1; xn = xn * xn % f; } mint ret = 0; for(int i=0; i<=a.deg(); i++) ret += a[i] * d[i]; return ret; } long long int dp[2][51][651]; long long int c[1251]; vector a = {2,3,5,7,11,13}; vector b = {4,6,8,9,10,12}; long long int n,p,q; vector v; long long int dp2[1251]; int main(void) { cin.tie(0); ios::sync_with_stdio(false); cin >> n >> p >> q; int m = p*a[5] + q*b[5]; dp[0][0][0] = 1; dp[1][0][0] = 1; for(int i=0;i=0;j--) { for(int k=0;k<=p*a[5];k++) { if(dp[0][j][k]==0) continue; for(int l=j+1;l<=p;l++) { if(k + (l-j)*a[i] > p*a[5]) break; dp[0][l][k + (l-j)*a[i]] += dp[0][j][k]; dp[0][l][k + (l-j)*a[i]]%=MOD; } } } } for(int i=0;i=0;j--) { for(int k=0;k<=q*b[5];k++) { if(dp[1][j][k]==0) continue; for(int l=j+1;l<=q;l++) { if(k + (l-j)*b[i] > q*b[5]) break; dp[1][l][k + (l-j)*b[i]] += dp[1][j][k]; dp[1][l][k + (l-j)*b[i]]%=MOD; } } } } for(int i=0;i<=p*a[5];i++) { for(int j=0;j<=q*b[5];j++) { if(i+j > m) continue; c[i+j] += ((dp[0][p][i]*dp[1][q][j])%MOD); c[i+j]%=MOD; } } dp2[0] = 1; for(int i=0;i<=m;i++) { for(int j=0;j<=m;j++) { if(i+j > m) break; dp2[i+j] += ((dp2[i]*c[j])%MOD); dp2[i+j]%=MOD; } } poly A,C; for(int i=0;i0;i--) { C.push_back(c[i]); } mint res = 0; long long int L = n - m; if(L < 0) L = 0; long long int R = n - 1; for(long long int i=L;i<=R;i++) { mint val = kitamasa(C,A,i); for(int j=0;j<=m;j++) { if(i+j >= n) { res += (val*(mint)c[j]); } } } cout << res << '\n'; return 0; }