题解

#include<cstring>
#include<iostream>
#include<cstdio>
#include<string>
#include<algorithm>
#include<vector>
using namespace std;
typedef long long LL;
const int B=35;
const int maxn=1e5+9;
const LL p=998244353;
inline int Read(){
int x(0),f(1); char c=getchar();
while(c<'0'||c>'9'){
if(c=='-') f=-1; c=getchar();
}
while(c>='0'&&c<='9')
x=(x<<3)+(x<<1)+c-'0',c=getchar();
return x*f;
}
bool visit[maxn];
int mu[maxn],phi[maxn],prime[maxn];
int *G[maxn],*S[B+1][B+1],F[maxn];
int inv[maxn];

inline void First(LL N){
mu[1]=phi[1]=inv[1]=1;
int tot(0);
for(int i=2;i<=N;++i){
if(!visit[i]){
prime[++tot]=i,
mu[i]=-1,
phi[i]=i-1;
}
for(int j=1;j<=tot&&iprime[j]<=N;++j){
visit[iprime[j]]=true;
if(i%prime[j]==0){
phi[iprime[j]]=phi[i]prime[j];
break;
}else{
phi[iprime[j]]=phi[i]phi[prime[j]],
mu[iprime[j]]=-mu[i];
}
}
}
for(int i=2;i<=N;++i)
inv[i]=p-1llp/iinv[p%i]%p;
for(int i=1;i<=N;++i)
for(int j=1;ji<=N;++j)
F[ij]=1ll(1llF[ij]+1lliinv[phi[i]]%pmu[j]%p)%p;
for(int i=1;i<=N;++i){
G[i]=new int [N/i+1];
G[i][0]=0;
for(int j=1;j<=N/i;++j)
G[i][j]=1ll(1llG[i][j-1]+1llphi[ji])%p;
}
for(int j=1;j<=B;++j)
for(int k=1;k<=B;++k){
int len(N/(max(j,k)));
S[j][k]=new int [len+1];
S[j][k][0]=0;
for(int i=1;i<=len;++i)
S[j][k][i]=1ll(1llS[j][k][i-1]+1llF[i]G[i][j]%pG[i][k]%p)%p;
}
}
inline LL Solve(int n,int m){
if(n>m)
swap(n,m);
LL ans(0);
for(int i=1;i<=m/B;++i)
ans=(ans+1llF[i]G[i][n/i]%pG[i][m/i]%p)%p;
for(int l=m/B+1,r;l<=n;l=r+1){
r=min(n/(n/l),m/(m/l));
ans=(ans+1ll(S[n/l][m/l][r]-S[n/l][m/l][l-1]+p)%p)%p;
}
return ans;
}
int main(){
int T=Read();
First(100000);
while(T--){
int n(Read()),m(Read());
printf("%lld\n",Solve(n,m));
}
return 0;
}