#ifndef call_from_test #include using namespace std; #define call_from_test #ifndef call_from_test #include using namespace std; using Int = long long; #endif //BEGIN CUT HERE template struct Mint{ static constexpr T mod = MOD; T v; Mint():v(0){} Mint(signed v):v(v){} Mint(long long t){v=t%MOD;if(v<0) v+=MOD;} Mint pow(long long k){ Mint res(1),tmp(v); while(k){ if(k&1) res*=tmp; tmp*=tmp; k>>=1; } return res; } static Mint add_identity(){return Mint(0);} static Mint mul_identity(){return Mint(1);} Mint inv(){return pow(MOD-2);} Mint& operator+=(Mint a){v+=a.v;if(v>=MOD)v-=MOD;return *this;} Mint& operator-=(Mint a){v+=MOD-a.v;if(v>=MOD)v-=MOD;return *this;} Mint& operator*=(Mint a){v=1LL*v*a.v%MOD;return *this;} Mint& operator/=(Mint a){return (*this)*=a.inv();} Mint operator+(Mint a) const{return Mint(v)+=a;}; Mint operator-(Mint a) const{return Mint(v)-=a;}; Mint operator*(Mint a) const{return Mint(v)*=a;}; Mint operator/(Mint a) const{return Mint(v)/=a;}; Mint operator-() const{return v?Mint(MOD-v):Mint(v);} bool operator==(const Mint a)const{return v==a.v;} bool operator!=(const Mint a)const{return v!=a.v;} bool operator <(const Mint a)const{return v constexpr T Mint::mod; template ostream& operator<<(ostream &os,Mint m){os<>h>>w>>k; using M = Mint; M ans{0}; for(int d=1;d class Enumeration{ private: static vector fact,finv,invs; public: static void init(int n){ n=min(n,M::mod-1); int m=fact.size(); if(n=m;i--) finv[i-1]=finv[i]*M(i); for(int i=m;i<=n;i++) invs[i]=finv[i]*fact[i-1]; } static M Fact(int n){ init(n); return fact[n]; } static M Finv(int n){ init(n); return finv[n]; } static M Invs(int n){ init(n); return invs[n]; } static M C(int n,int k){ if(n > D(int n,int m){ vector< vector > dp(n+1,vector(m+1,0)); dp[0][0]=M(1); for(int i=0;i<=n;i++){ for(int j=1;j<=m;j++){ if(i-j>=0) dp[i][j]=dp[i][j-1]+dp[i-j][j]; else dp[i][j]=dp[i][j-1]; } } return dp; } static M B(int n,int k){ if(n==0) return M(1); k=min(k,n); init(k); vector dp(k+1); dp[0]=M(1); for(int i=1;i<=k;i++) dp[i]=dp[i-1]+((i&1)?-finv[i]:finv[i]); M res(0); for(int i=1;i<=k;i++) res+=M(i).pow(n)*finv[i]*dp[k-i]; return res; } static M montmort(int n){ init(n); M res(0); for(int k=2;k<=n;k++){ if(k&1) res-=finv[k]; else res+=finv[k]; } return res*=fact[n]; } static M LagrangePolynomial(vector &y,M t){ int n=y.size()-1; if(t.v<=n) return y[t.v]; init(n+1); vector dp(n+1,1),pd(n+1,1); for(int i=0;i0;i--) pd[i-1]=pd[i]*(t-M(i)); M res(0); for(int i=0;i<=n;i++){ M tmp=y[i]*dp[i]*pd[i]*finv[i]*finv[n-i]; if((n-i)&1) res-=tmp; else res+=tmp; } return res; } }; template vector Enumeration::fact=vector(); template vector Enumeration::finv=vector(); template vector Enumeration::invs=vector(); //END CUT HERE #ifndef call_from_test #define call_from_test #ifndef call_from_test #include using namespace std; using Int = long long; #endif //BEGIN CUT HERE template map factorize(T x){ map res; for(int i=2;i*i<=x;i++){ while(x%i==0){ x/=i; res[i]++; } } if(x!=1) res[x]++; return res; } //END CUT HERE #ifndef call_from_test //INSERT ABOVE HERE signed main(){ int a,b; cin>>a>>b; map m; for(int i=b+1;i<=a;i++){ auto x=factorize(i); for(auto p:x) m[p.first]+=p.second; } const Int MOD = 1e9+7; Int ans=1; for(auto p:m) (ans*=(p.second+1))%=MOD; cout<; using E = Enumeration; M m; scanf("%d %d",&n,&m.v); E::init(n+100); Mint ans(1); auto x=factorize(m.v); for(auto p:x) ans*=E::H(n,p.second); printf("%d\n",ans.v); return 0; } /* verified on 2019/10/08 https://atcoder.jp/contests/abc110/tasks/abc110_d */ //montmort signed ARC009_C(){ long long n,k; scanf("%lld %lld",&n,&k); const int MOD = 1777777777; using M = Mint; using E = Enumeration; M a=E::montmort(k)*M::comb(n,k); printf("%lld\n",a.v); return 0; } /* verified on 2019/10/08 https://atcoder.jp/contests/arc009/tasks/arc009_3 */ signed ARC033_D(){ int n; scanf("%d",&n); using M = Mint; using E = Enumeration; vector y(n+1); for(int i=0;i<=n;i++) scanf("%d",&y[i].v); int t; scanf("%d",&t); printf("%d\n",E::LagrangePolynomial(y,M(t)).v); return 0; } /* verified on 2019/10/08 https://atcoder.jp/contests/arc033/tasks/arc033_4 */ signed YUKI_117(){ int T; scanf("%d\n",&T); using M = Mint; using E = Enumeration; E::init(2e6+100); while(T--){ char c; int n,k; scanf("%c(%d,%d)\n",&c,&n,&k); if(c=='C') printf("%d\n",E::C(n,k).v); if(c=='P') printf("%d\n",E::P(n,k).v); if(c=='H') printf("%d\n",E::H(n,k).v); } return 0; } /* verified on 2019/10/08 https://yukicoder.me/problems/no/117 */ signed YUKI_042(){ using M = Mint; using E = Enumeration; const int MAX = 666 * 6 + 10; vector dp(MAX,0); dp[0]=M(1); for(int x:{1,5,10,50,100,500}) for(int j=x;j y(6); for(int i=0;i<6;i++) y[i]=dp[(m%500)+(i*500)]; M ans=E::LagrangePolynomial(y,M(m/500)); printf("%d\n",ans.v); } return 0; } /* verified on 2019/10/08 https://yukicoder.me/problems/no/42 */ signed CFR315_B(){ cin.tie(0); ios::sync_with_stdio(0); int n; cin>>n; using M = Mint; using E = Enumeration; E::init(n+1); M res; for(int i=0;i