题目：

 

解：神仙 题  化出了式子了 还要会构造函数，构造了函数 还要会实现。  牛逼儿~~~   （ 出处：）

 

 

 

 

#include
      
       #define LL long long#define ULL unsigned long long#define rep(i,j,k) for(int i=j;i<=k;i++)#define dep(i,j,k) for(int i=k;i>=j;i--)#define INF 0x3f3f3f3f#define mem(i,j) memset(i,j,sizeof(i))#define make(i,j) make_pair(i,j)#define pb push_backusing namespace std;const int block=35;const int N=1e5+9;const LL p=998244353;bool vis[N];int mu[N],phi[N],pre[N];int *G[N],*S[block+1][block+1],F[N];int inv[N],tot;void init() {    mu[1]=phi[1]=inv[1]=1;    rep(i,2,100000) {        if(!vis[i]) {            pre[++tot]=i; mu[i]=-1; phi[i]=i-1;        }        rep(j,1,tot) {            if(i*pre[j]>100000) break;            vis[i*pre[j]]=true;            if(i%pre[j]==0) {                phi[i*pre[j]]=phi[i]*pre[j]; break;            }            else {                phi[i*pre[j]]=phi[i]*phi[pre[j]];                mu[i*pre[j]]=-mu[i];            }        }    }    rep(i,2,100000) inv[i]=p-1LL*p/i*inv[p%i]%p;    rep(i,1,100000) {        for(int j=1;j*i<=100000;j++) {            F[i*j]=1LL*(1LL*F[i*j]+1LL*i*inv[phi[i]]%p*mu[j]%p)%p;        }    }    rep(i,1,100000) {        G[i]=new int [N/i+1];        G[i][0]=0;        rep(j,1,100000/i) {            G[i][j]=1LL*(1LL*G[i][j-1]+1LL*phi[i*j])%p;        }    }    rep(j,1,block) {        rep(k,1,block) {            int len(100000/(max(k,j)));            S[j][k]=new int [len+1];            S[j][k][0]=0;            rep(i,1,len) {                S[j][k][i]=1LL*(1LL*S[j][k][i-1]+1LL*F[i]*G[i][j]%p*G[i][k]%p)%p;            }        }    }}LL cal(int n,int m) {    if(n>m) swap(n,m);    LL ans=0;    for(int i=1;i<=m/block;i++) ans=(ans+1LL*F[i]*G[i][n/i]%p*G[i][m/i]%p)%p;    for(int l=m/block+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() {    init();    int t;    scanf("%d",&t);    while(t--) {        int n,m;        scanf("%d %d",&n,&m);        printf("%lld\n",cal(n,m));    }    return 0;}