//Let's join Kaede Takagaki Fan Club !! #include #include #include using namespace std; typedef long long ll; typedef pair P; typedef pair P1; typedef pair P2; #define pu push #define pb push_back #define mp make_pair #define eps 1e-7 #define INF 1000000000 #define fi first #define sc second #define rep(i,x) for(int i=0;i void dmp(T a){ rep(i,a.size()) cout << a[i] << " "; cout << endl; } template bool chmax(T&a, T b){ if(a < b){ a = b; return 1; } return 0; } template bool chmin(T&a, T b){ if(a > b){ a = b; return 1; } return 0; } template void g(T &a){ cin >> a; } template void o(const T &a,bool space=false){ cout << a << (space?' ':'\n'); } //ios::sync_with_stdio(false); const int mod = 1000000007;//998244353 template void add(T&a,T b){ a+=b; while(a >= mod) a-=mod; while(a < 0) a += mod; } template struct ntt{ inline void add(int &a, int b) { a += b; if(a >= md) a -= md; } inline void sub(int &a, int b) { a -= b; if(a < 0) a += md; } inline int add2(int a, int b) { a += b; if(a >= md) a -= md; return a;} inline int sub2(int a, int b) { a -= b; if(a < 0) a += md; return a;} inline int mul(int a, int b) { return (int)((ll)a*b%md); } inline int power(int a, long long b) { int res = 1; while (b > 0) { if (b & 1) res = mul(res, a); a = mul(a, a); b >>= 1; } return res; } inline int inv(int a) { a %= md; if (a < 0) a += md; int b = md, u = 0, v = 1; while (a) { int t = b / a; b -= t * a; swap(a, b); u -= t * v; swap(u, v); } assert(b == 1); if (u < 0) u += md; return u; } int max_base, root; vector dw, idw; ntt() { int tmp = md - 1; max_base = 0; while (tmp % 2 == 0) { tmp /= 2; max_base++; } root = 2; while (power(root, (md-1)>>1) == 1) root++; dw.resize(max_base); idw.resize(max_base); rep(i, max_base){ sub(dw[i], power(root, (md-1) >> (i+2))); idw[i] = inv(dw[i]); } } void fft(vector &a, bool inv) { const int n = a.size(); assert((n & (n - 1)) == 0); assert(__builtin_ctz(n) <= max_base); if(!inv){ for(int m=n;m>>=1;){ int w = 1; for(int s=0,k=0; s=y?x-y:x+md-y); a[i] = (x+y>=md?x+y-md:x+y); } w = mul(w, dw[__builtin_ctz(++k)]); } } } else{ for(int m=1;m=y?x-y:x+md-y); a[j] = mul(a[j], w); a[i] = (x+y>=md?x+y-md:x+y); } w = mul(w, idw[__builtin_ctz(++k)]); } } const int inv_sz = this->inv(n); for(auto &&e:a) e = mul(e, inv_sz); } } vector multiply(vector a, vector b, int eq = 0) { int need = a.size() + b.size() - 1; int nbase = 0; while ((1 << nbase) < need) nbase++; int sz = 1 << nbase; a.resize(sz); b.resize(sz); fft(a, 0); if (eq) b = a; else fft(b, 0); rep(i, sz) a[i] = mul(a[i], b[i]); fft(a, 1); a.resize(need); return a; } vector square(vector a) { return multiply(a, a, 1); } }; //fast_ntt.cpp /* 167772161; //= 2^25 * 5 + 1 469762049; //= 2^26 * 7 + 1 754974721; //= 2^24 * 45 + 1 1045430273; //= 2^20 * 997 + 1 1051721729; //= 2^20 * 1003 + 1 1053818881; //= 2^20 * 1005 + 1 */ template vector anyntt(vector&a, vector&b, int eq = 0) { //今回は2^20以下だからこっちの方が速い (らしい) (:maroon_kansha:) const int m1 = 167772161, m2 = 469762049, m3 = 754974721; nttn1; nttn2; nttn3; nttnn; auto a1 = n1.multiply(a, b, eq); auto a2 = n2.multiply(a, b, eq); auto a3 = n3.multiply(a, b, eq); const int n = a1.size(); vectorret(n); vectorm; m = {m1, m2, m3}; vectorr; r = {1, n2.inv(m1), n3.inv(n3.mul(m1, m2))}; int mm = nn.mul(m1, m2); rep(i, n){ n2.add(a2[i], n2.sub2(m2, a1[i])); int v1 = n2.mul(a2[i], r[1]); n3.add(a3[i], n3.sub2(m3, n3.add2(a1[i], n3.mul(m1, v1)))); int v2 = n3.mul(a3[i], r[2]); nn.add(a1[i], nn.add2(nn.mul(m1, v1), nn.mul(mm, v2))); ret[i] = a1[i]; } return ret; } ll modpow(ll x,ll n){ ll res=1; while(n>0){ if(n&1) res=res*x%mod; x=x*x%mod; n>>=1; } return res; } typedef vector vi; vi shrink(vi a){ while(a.size() && a.back() == 0) a.pop_back(); return a; } vi mul_int(vi a, int M){ for(auto &b: a) b = (int)((ll)(b) * M) % mod; return a; } vi mul(vi a, vi b, int eq = 0){ return anyntt(a, b, eq); //kaede.multiply(a, b, eq); } vi add(vi a, vi b,int M=-1){ if(a.size() < b.size()) swap(a,b); for(int i=0;i= mod) a[i] -= mod; } if(M >= 0 && a.size() > M) a.resize(M); return a; } vi sub(vi a, vi b,int M=-1){ if(a.size() < b.size()) a.resize(b.size(), 0); for(int i=0;i= mod) a[i] -= mod; } if(M >= 0 && a.size() > M) a.resize(M); return a; } vi lw(vi a, int x){ if(a.size() > x) a.resize(x); return a; } /*vi inv(vi a,int M){ if(a.empty() || a[0] == 0) return vi(); vi ret(1); ret[0] = modpow(a[0],mod-2); int cur = 1; int nxt = 1; while(cur < M){ auto g = lw(ret, cur); auto f = lw(a, cur*2); f.resize(cur << 1); g.resize(cur << 1); kaede.fft(f, 0); kaede.fft(g, 0); rep(i, f.size()) f[i] = kaede.mul(f[i], g[i]); kaede.fft(f, 1); f.erase(begin(f), begin(f) + cur); f.resize(cur << 1), kaede.fft(f, 0); rep(i, f.size()) { f[i] = mod - kaede.mul(f[i], g[i]); } kaede.fft(f, 1); ret.insert(end(ret), begin(f), begin(f)+ cur); nxt++; cur <<= 1; } assert(ret.size() >= M); ret.resize(M); return ret; }*/ //slow vi inv(vi a,int M){ if(a.empty() || a[0] == 0) return vi(); vi ret(M); ret[0] = modpow(a[0],mod-2); int cur = 1; int nxt = 1; while(cur < M){ auto at = lw(ret, cur); ret = sub(add(at, at), mul(mul(at, at, 1), lw(a, cur*2))); ret.resize(cur << 1); nxt++; cur <<= 1; } assert(ret.size() >= M); ret.resize(M); return ret; } vi modpow(vi a, ll n, vi b){ vi rb = b; reverse(all(rb)); rb = inv(rb, rb.size()); auto get_mod = [&](vi v){ vi dv, u = v; if(v.size() < b.size()) dv = {}; else{ int sz = v.size() - b.size() + 1; vi y = lw(rb, sz); reverse(all(v)); v = lw(v, sz); dv = mul(v, y); dv.resize(sz); reverse(all(dv)); } u = sub(u, mul(dv, b)); return shrink(u); }; if(a.size() >= b.size()){ a = get_mod(a); } assert(a.size() < b.size()); vi ret = {1}; while(n){ if(n & 1){ ret = mul(ret, a); ret = get_mod(ret); } n >>= 1; a = mul(a, a, 1); a = get_mod(a); } return ret; } template vectorBerlekampMassey(vectorx){ vectorls,cur; T lf,ld; rep(i,x.size()){ T t = 0; for(int j=0;jc(i-lf-1); c.pb(k); rep(j,ls.size()) c.pb((ll)-ls[j]*k%mod); if(c.size() < cur.size()) c.resize(cur.size()); rep(j,cur.size()){ c[j]=(c[j]+cur[j]); while(c[j] < 0) c[j] += mod; while(c[j] >= mod) c[j] -= mod; } if(i-lf+(int)(ls.size()) >= (int)(cur.size())){ ls = cur, lf = i, ld = (t-x[i])%mod; } cur = c; } rep(i,cur.size()) cur[i] = (cur[i]%mod+mod)%mod; return cur; } inline int mul(int a, int b) {return ((ll)a * b % mod); } typedef vector vi; ll n; int p, c, dp[2][305][3905]; vi f; int v[2][6] = {{2, 3, 5, 7, 11, 13}, {4, 6, 8, 9, 10, 12}}; void make(int id){ dp[id][0][0] = 1; for(int x=0;x<6;x++){ rep(i, 300){ rep(j, 3900){ if(dp[id][i][j] == 0) continue; add(dp[id][i+1][j+v[id][x]], dp[id][i][j]); } } } } int main(){ scanf("%lld%d%d",&n, &p, &c); make(0); make(1); f.resize(p*13 + c*12 + 1); rep(i, 3905) rep(j, 3905){ if(dp[0][p][i] == 0 || dp[1][c][j] == 0) continue; add(f[i+j], mul(dp[0][p][i], dp[1][c][j])); } for(auto &a:f) a = (mod-a)%mod; f[0] = 1; int A = p*13 + c*12; auto ans = inv(f, 3*A); auto g = f; reverse(all(g)); int ret = 0; if(n <= 3*A){ for(int j=max(0, (int)n-A);j < n;j++){ int coef = 0; for(int k=1;k<=A;k++){ if(j+k >= n){ add(coef, mod-f[k]); } add(ret, mul(ans[j], coef)); } } printf("%d\n", ret); } else{ auto v = modpow({0, 1}, n-A, g); for(ll j=n-A;j= n){ add(coef, mod-f[k]); } } add(ret, mul(M, coef)); } printf("%d\n", ret); } }