F. Rhyme scheme

#include<bits/stdc++.h>
using namespace std;
typedef __int128 ll;
const int M=30;
const int mod=1e9+7;
ll dp[M][M];
int a[M];
int n;

inline ll read() {
    ll x = 0, f = 1;
    char c = getchar();
    for (; !isdigit(c);c = getchar()) if (c == ‘-‘) f = -1;
    for (; isdigit(c); c = getchar()) x = x * 10 + c - ‘0‘;
    return x * f;
}
ll dfs1(int pos,int up){
    if(pos==n+1)
        return 1;
    if(~dp[pos][up])
        return dp[pos][up];
    ll sum=0;
    for(int i=0;i<=up;i++){
        sum+=dfs1(pos+1,max(up,i+1));
    }
    dp[pos][up]=sum;
    return sum;
}
void dfs2(int pos,int up,ll r){
    if(pos==n+1){
        for(int i=1;i<=n;i++)
            putchar(a[i]+‘A‘);
        puts("");
        return ;
    }
    for(int i=0;i<=up;i++){
        int nowup=max(i+1,up);
        if(r<=dp[pos+1][nowup]){
            a[pos]=i;
            dfs2(pos+1,nowup,r);
            break;
        }
        else
            r-=dp[pos+1][nowup];
    }
}
int main(){
    int t;
    scanf("%d",&t);
    for(int ca=1;ca<=t;ca++){
        scanf("%d",&n);
        ll k=read();
        for(int i=0;i<M;i++)
            for(int j=0;j<M;j++)
                dp[i][j]=-1;
        for(int i=0;i<M;i++)
            dp[n+1][i]=1;
    //    cout<<"!!"<<endl;
        dfs1(1,0);
        printf("Case #%d: ",ca);
        dfs2(1,0,k);
    }
    return 0;
}