毒瘤之神的考验

#include <cstdio>
#include <cmath>
#include <algorithm>
using namespace std;
#define ll long long
#define re register
const int p=998244353;
const int B=35;
const int N=1e5+10;
const int M=1e5;
void read(int &a)
{
    int d=1;
    a=0;
    char ch;
    while(ch=getchar(),ch>‘9‘||ch<‘0‘)
        if(ch==‘-‘)
            d=-1;
    a=ch^48;
    while(ch=getchar(),ch>=‘0‘&&ch<=‘9‘)
        a=(a<<3)+(a<<1)+(ch^48);
    a*=d;
}
int phi[N],mu[N],pri[N],cnt,inv[N];
ll *G[N],F[N],*S[B+1][B+1];
bool vis[N];
inline void init()
{
    inv[1]=phi[1]=mu[1]=1;
    for(re int i=2;i<=M;i++)
    {
        if(!vis[i])
            pri[++cnt]=i,mu[i]=-1,phi[i]=i-1;
        for(re int j=1;j<=cnt&&i*pri[j]<=M;j++)
        {
            vis[i*pri[j]]=1;
            if(i%pri[j]==0)
            {
                phi[i*pri[j]]=phi[i]*pri[j];
                break;
            }
            mu[i*pri[j]]=-mu[i];
            phi[i*pri[j]]=phi[i]*(pri[j]-1);
        }
    }
    for(re int i=2;i<=M;i++)
        inv[i]=1ll*(p-p/i)*inv[p%i]%p;
    for(re int i=1;i<=M;i++)///枚举因子 (nlogn筛出F[x])
        for(re int j=1;j*i<=M;j++)
            F[i*j]=(F[i*j]+1ll*(i*mu[j]%p)*inv[phi[i]]%p)%p;
    for(re int i=1;i<=M;i++)
    {
        G[i]=new ll [M/i+1];
        G[i][0]=0;
        for(re int j=1;j<=M/i;j++)
            G[i][j]=(G[i][j-1]+phi[i*j]);
    }
    for(re int j=1;j<=B;j++)
        for(re int k=1;k<=B;k++)
        {
            ll len=M/max(j,k);
            S[j][k]=new ll [len+1];
            S[j][k][0]=0;
            for(re int i=1;i<=len;i++)
                S[j][k][i]=(S[j][k][i-1]+(F[i]*G[i][j])%p*G[i][k]%p)%p;
        }
}
inline ll solve(int n,int m)
{
    if(n>m)
        swap(n,m);
    ll ans=0;
    for(re int i=1;i<=m/B;i++)
        ans=(ans+(F[i]*G[i][n/i]%p)*G[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+(S[n/l][m/l][r]-S[n/l][m/l][l-1]+p)%p)%p;
    }
    return ans;
}
int main()
{
    init();
    int T;
    read(T);
    while(T--)
    {
        int n,m;
        read(n);
        read(m);
        printf("%lld\n",solve(n,m));
    }
    return 0;
}