#include using namespace std; #define REP(i,a,b) for(i=a;i'9')break;*x=(*x)*10+k-'0';}if(m)(*x)=-(*x);} void reader(ll *x){int k,m=0;*x=0;for(;;){mygc(k);if(k=='-'){m=1;break;}if('0'<=k&&k<='9'){*x=k-'0';break;}}for(;;){mygc(k);if(k<'0'||k>'9')break;*x=(*x)*10+k-'0';}if(m)(*x)=-(*x);} void reader(double *x){scanf("%lf",x);} int reader(char c[]){int i,s=0;for(;;){mygc(i);if(i!=' '&&i!='\n'&&i!='\r'&&i!='\t'&&i!=EOF) break;}c[s++]=i;for(;;){mygc(i);if(i==' '||i=='\n'||i=='\r'||i=='\t'||i==EOF) break;c[s++]=i;}c[s]='\0';return s;} template void reader(T *x, S *y){reader(x);reader(y);} template void reader(T *x, S *y, U *z){reader(x);reader(y);reader(z);} template void reader(T *x, S *y, U *z, V *w){reader(x);reader(y);reader(z);reader(w);} void writer(int x, char c){int s=0,m=0;char f[10];if(x<0)m=1,x=-x;while(x)f[s++]=x%10,x/=10;if(!s)f[s++]=0;if(m)mypc('-');while(s--)mypc(f[s]+'0');mypc(c);} void writer(ll x, char c){int s=0,m=0;char f[20];if(x<0)m=1,x=-x;while(x)f[s++]=x%10,x/=10;if(!s)f[s++]=0;if(m)mypc('-');while(s--)mypc(f[s]+'0');mypc(c);} void writer(double x, char c){printf("%.15f",x);mypc(c);} void writer(const char c[]){int i;for(i=0;c[i]!='\0';i++)mypc(c[i]);} void writer(const char x[], char c){int i;for(i=0;x[i]!='\0';i++)mypc(x[i]);mypc(c);} template void writerLn(T x){writer(x,'\n');} template void writerLn(T x, S y){writer(x,' ');writer(y,'\n');} template void writerLn(T x, S y, U z){writer(x,' ');writer(y,' ');writer(z,'\n');} template void writerArr(T x[], int n){int i;if(!n){mypc('\n');return;}rep(i,n-1)writer(x[i],' ');writer(x[n-1],'\n');} struct mint{ static unsigned md, W, R, Rinv, mdninv, RR; unsigned val; mint(){} mint(int a){val = mulR(a);} mint(unsigned a){val = mulR(a);} mint(ll a){val = mulR(a);} mint(ull a){val = mulR(a);} unsigned setmod(unsigned m){ W = 32; md = m; R = (1ULL << W) % md; RR = (ull)R*R % md; switch(m){ case 998244353: Rinv = 232013824; mdninv = 998244351; break; case 1000000007: Rinv = 518424770; mdninv = 2226617417U; break; case 1000000009: Rinv = 171601999; mdninv = 737024967; break; case 1004535809: Rinv = 234947584; mdninv = 1004535807; break; case 1007681537: Rinv = 236421376; mdninv = 1007681535; break; case 1012924417: Rinv = 238887936; mdninv = 1012924415; break; case 1045430273: Rinv = 254466304; mdninv = 1045430271; break; case 1051721729: Rinv = 257538304; mdninv = 1051721727; break; } } unsigned mulR(unsigned a){ return (ull)a*R%md; } unsigned mulR(int a){ if(a < 0) a = a%md+md; return mulR((unsigned)a); } unsigned mulR(ull a){ return mulR((unsigned)(a%md)); } unsigned mulR(ll a){ if(a < 0) a = a%md+md; return mulR((unsigned)a); } unsigned reduce(unsigned T){ unsigned m = T * mdninv; unsigned t = (unsigned)((T + (ull)m*md) >> W); if(t >= md) t -= md; return t; } unsigned reduce(ull T){ unsigned m = (unsigned)T * mdninv; unsigned t = (unsigned)((T + (ull)m*md) >> W); if(t >= md) t -= md; return t; } unsigned get(){ return reduce(val); } mint &operator+=(mint a){ val += a.val; if(val >= md) val -= md; return *this; } mint &operator-=(mint a){ if(val < a.val) val = val + md - a.val; else val -= a.val; return *this; } mint &operator*=(mint a){ val = reduce((ull)val*a.val); return *this; } mint &operator/=(mint a){ return *this *= a.inverse(); } mint operator+(mint a){ return mint(*this)+=a; } mint operator-(mint a){ return mint(*this)-=a; } mint operator*(mint a){ return mint(*this)*=a; } mint operator/(mint a){ return mint(*this)/=a; } mint inverse(){ int a = val, b = md, u = 1, v = 0, t; mint res; while(b){ t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } if(u < 0) u += md; res.val = (ull)u*RR % md; return res; } mint pw(ull b){ mint a(*this), res; res.val = R; while(b){ if(b&1) res *= a; b >>= 1; a *= a; } return res; } }; unsigned mint::md, mint::W, mint::R, mint::Rinv, mint::mdninv, mint::RR; ull pw(ull a, ull b, ull m){ull r=1;while(b){if(b&1)r=r*a%m;b>>=1;a=a*a%m;}return r;} void mfft(int n, mint x[], mint root, void *mem){ int i, j; int n1, n2, n3, step = 1; mint w1, w2, w3, a, b, c, d, aa, bb, cc, dd, tmp, *y = (mint*)mem; tmp = root.pw((mint::md-1)/4*3); root = root.pw((mint::md-1)/n); while(n > 2){ n1 = n / 4; n2 = n1 + n1; n3 = n1 + n2; w1.val = mint::R; rep(i,n1){ w2 = w1*w1; w3 = w1*w2; rep(j,step){ a = x[j+step*i]; b = x[j+step*(i+n1)]; c = x[j+step*(i+n2)]; d = x[j+step*(i+n3)]; aa = a + c; bb = a - c; cc = b + d; dd = (b - d) * tmp; y[j+step*(4*i )] = aa + cc; y[j+step*(4*i+1)] = w1*(bb - dd); y[j+step*(4*i+2)] = w2*(aa - cc); y[j+step*(4*i+3)] = w3*(bb + dd); } w1 *= root; } n /= 4; step *= 4; root *= root; root *= root; swap(x,y); } if(n==2){ rep(i,step){ y[i] = x[i] + x[i+step]; y[i+step] = x[i] - x[i+step]; } n /= 2; step *= 2; root *= root; swap(x,y); } rep(i,step) y[i] = x[i]; } void mfftinv(int n, mint x[], mint root, void *mem){ int i, j; int n1, n2, n3, step = 1; mint w1, w2, w3, a, b, c, d, aa, bb, cc, dd, tmp, *y = (mint*)mem; root = root.inverse(); tmp = root.pw((mint::md-1)/4); root = root.pw((mint::md-1)/n); while(n > 2){ n1 = n / 4; n2 = n1 + n1; n3 = n1 + n2; w1.val = mint::R; rep(i,n1){ w2 = w1*w1; w3 = w1*w2; rep(j,step){ a = x[j+step*i]; b = x[j+step*(i+n1)]; c = x[j+step*(i+n2)]; d = x[j+step*(i+n3)]; aa = a + c; bb = a - c; cc = b + d; dd = (b - d) * tmp; y[j+step*(4*i )] = aa + cc; y[j+step*(4*i+1)] = w1*(bb + dd); y[j+step*(4*i+2)] = w2*(aa - cc); y[j+step*(4*i+3)] = w3*(bb - dd); } w1 *= root; } n /= 4; step *= 4; root *= root; root *= root; swap(x,y); } if(n==2){ rep(i,step){ y[i] = x[i] + x[i+step]; y[i+step] = x[i] - x[i+step]; } n /= 2; step *= 2; root *= root; swap(x,y); } rep(i,step) y[i] = x[i]; } void gmodcomvolutionsGetData(int num, int md[], int root[], int inv[]){ int i, j, k; static int d_md[5] = {1004535809,1007681537,1012924417,1045430273,1051721729}; static int d_rt[5] = {3,3,5,3,6}; static int d_iv[5][5] = {{},{335894166},{253231225,405169960},{26805930,551754894,843088962},{303830744,325532940,568498259,175287122}}; rep(i,num) md[i] = d_md[i]; rep(i,num) root[i] = d_rt[i]; rep(i,num) rep(j,i) inv[i*num+j] = d_iv[i][j]; } template void gmodconvolution(S A[], int As, T B[], int Bs, U res[], int Rs, void *mem, int md, int num=3){ int i, j, k, m, n, n2; mint r, rt; int *tmd, *trt, *tiv, *val; mint **a; val = (int*)mem; tmd = val+num; trt = tmd+num; tiv = trt+num; gmodcomvolutionsGetData(num, tmd, trt, tiv); n = max(As+Bs, Rs); for(n2=1;n2=0;i--){ k = ((ll)k*tmd[i] + val[i]) % md; } res[m] = k; } } template void gmodconvolution(S A[], int As, T res[], int Rs, void *mem, int md, int num=3){ int i, j, k, m, n, n2; mint r, rt; int *tmd, *trt, *tiv, *val; mint **a; val = (int*)mem; tmd = val+num; trt = tmd+num; tiv = trt+num; gmodcomvolutionsGetData(num, tmd, trt, tiv); n = max(As+As, Rs); for(n2=1;n2=0;i--){ k = ((ll)k*tmd[i] + val[i]) % md; } res[m] = k; } } template void gmodconvolutionPreCalc(S A[], int As, mint res[], int Rs, void *mem, int md, int num=3, int domultiply=1){ int i, j, n2; mint r, rt; int *tmd, *trt, *tiv, *val; mint *a; val = (int*)mem; tmd = val+num; trt = tmd+num; tiv = trt+num; gmodcomvolutionsGetData(num, tmd, trt, tiv); n2 = Rs; a = (mint*)(tiv+num*num); mem = a+n2; rep(j,num){ r.setmod(tmd[j]); rep(i,As) a[i] = A[i]; REP(i,As,n2) a[i].val = 0; rt = trt[j]; mfft(n2, a, rt, mem); rep(i,Rs) res[j*Rs+i] = a[i]; if(domultiply){ r = mint(n2).inverse(); rep(i,Rs) res[j*Rs+i] *= r; } } } template void gmodconvolutionWithPreCalc(mint A[], int As, T B[], int Bs, U res[], int Rs, void *mem, int md, int num=3, int ordered=1, int domultiply=0){ int i, j, n2, k, m; mint r, rt; int *tmd, *trt, *tiv, *val; mint **a; val = (int*)mem; tmd = val+num; trt = tmd+num; tiv = trt+num; gmodcomvolutionsGetData(num, tmd, trt, tiv); n2 = As; a = (mint**)(tiv+num*num); a[0] = (mint*)(a+num+1); REP(i,1,num+1) a[i] = a[i-1] + n2; mem = a[num]+n2; rep(j,num){ r.setmod(tmd[j]); rep(i,n2) a[j][i] = A[j*n2+i]; rep(i,Bs) a[num][i] = B[i]; REP(i,Bs,n2) a[num][i].val = 0; rt = trt[j]; mfft(n2, a[num], rt, mem); rep(i,n2) a[j][i] *= a[num][i]; mfftinv(n2, a[j], rt, mem); if(domultiply){ r = mint(n2).inverse(); rep(i,Rs) a[j][i] *= r; } rep(i,Rs) a[j][i].val = a[j][i].get(); } rep(m,Rs){ rep(i,num) val[i] = a[i][m].val; rep(i,num) rep(j,i){ k = val[i] - val[j]; if(k < 0) k += tmd[i]; val[i] = (ll)k*tiv[i*num+j]%tmd[i]; } k = 0; for(i=num-1;i>=0;i--){ k = ((ll)k*tmd[i] + val[i]) % md; } res[m] = k; } } int modconvolutionGetLength(int As, int Bs, int Rs){int n=max(As+Bs,Rs),res;for(res=1;res void Kitamasa_g_reduce(int a[], int sz, T c[], int d, int md, ll limit, int num, int calsz, mint **calc, int *beflen, int *aftlen, void *mem){ int i, j, st, len, ex; int *D = (int*)mem; ll *arr = (ll*)(D+2*d); mem = (void*)(arr + sz); rep(i,sz) arr[i] = a[i]; for(j=calsz-1;j>=0;j--){ ex = sz - d; len = beflen[j] - d; if(ex < 2*len) continue; st = ex - 2*len; gmodconvolutionWithPreCalc(calc[j], aftlen[j], arr+sz-len, len, D, d+len, mem, md, num); rep(i,d+len){ arr[st+i+1] += D[i]; if(arr[st+i] >= md) arr[st+i] -= md; } sz -= len; } while(sz > d){ sz--; if(arr[sz] >= md) arr[sz] %= md; rep(i,d){ arr[sz-d+i] += arr[sz] * c[i]; if(arr[sz-d+i] >= limit) arr[sz-d+i] %= md; } } rep(i,sz){ if(arr[i] >= md) arr[i] %= md; } rep(i,sz) a[i] = arr[i]; } template ll Kitamasa_g(ll n, S a[], T c[], int d, int md, void *mem){ int i, j, m, len, st; ll limit = ((1ULL<<63)-1)-(ull)(md-1)*(md-1); ll *arr; int sz, s; int *A; int *D, *E; int reduce_size = 0; int *reduce_len; int *reduce_calc_len; mint **reduce_calc; ll C; int num; double chk; if(n < d) return a[n]; chk = (log(2) + log(d) + 2 * log(md)) / log(1004535809); num = ceil(chk+1e-5); reduce_len = (int*)mem; reduce_calc_len = reduce_len + 25; reduce_calc = (mint**)(reduce_calc_len+25); A = (int*)(reduce_calc+25); mem = A + 2*d; for(i=20;i>=0;i--) if(d/(1<= 500 || i==0){ m = d + d/(1<= md) D[st+i] -= md; } s -= len; } rep(i,2*d) A[i] = D[i]; if(arr[sz]!=arr[sz+1]*2){ C = A[2*d-1]; for(i=2*d-1;i;i--) A[i] = A[i-1]; A[0] = 0; rep(i,d) A[d+i] = (A[d+i] + c[i] * C) % md; } } Kitamasa_g_reduce(A, 2*d, c, d, md, limit, num, reduce_size, reduce_calc, reduce_len, reduce_calc_len, mem); C = 0; rep(i,d){ C += (ll)a[i] * A[i]; if(C>=limit)C%=md; } if(C >= md) C %= md; return C; } char memarr[127000000]; void *mem = memarr; #define MD 1000000007 int pp[6] = {2,3,5,7,11,13}; int cc[6] = {4,6,8,9,10,12}; ll dp_p[301][4200], dp_c[301][4200]; ll a[9400], c[9400]; int main(){ int i, j, k, d; ll N; int P, C; int res; if(0){ int a[100000], b[100000], c[200000]; rep(i,100000) a[i] = b[i] = (1e8) + i; gmodconvolution(a,100000,c,200000,mem,MD); writerLn(c[12345]); return 0; } dp_p[0][0] = dp_c[0][0] = 1; rep(k,6) rep(i,300) rep(j,4200) if(dp_p[i][j]) dp_p[i+1][j+pp[k]] = (dp_p[i+1][j+pp[k]] + dp_p[i][j]) % MD; rep(k,6) rep(i,300) rep(j,4200) if(dp_c[i][j]) dp_c[i+1][j+cc[k]] = (dp_c[i+1][j+cc[k]] + dp_c[i][j]) % MD; reader(&N); reader(&P, &C); d = P * pp[5] + C * cc[5]; rep(i,d) a[i] = 1; rep(i,4200) if(dp_p[P][i]) rep(j,4200) if(dp_c[C][j]) c[d-i-j] = (c[d-i-j] + (ll)dp_p[P][i] * dp_c[C][j]) % MD; res = Kitamasa_g(N+d-1, a, c, d, MD, mem); writer(res, '\n'); return 0; }