Rhyme scheme

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•  1000ms
•  65536K

 

A rhyme scheme is the pattern of rhymes at the end of each line of a poem or song. It is usually referred to by using letters to indicate which lines rhyme; lines designated with the same letter all rhyme with each other.

e.g., the following "poem'' of 44 lines has an associated rhyme scheme "ABBA''

1 —— 9999 bugs in the code A

2 —— Fix one line B

3 —— Should be fine B

4 —— 100100 bugs in the code A

This essentially means that line 11 and 44 rhyme together and line 22 and 33 rhyme together.

The number of different possible rhyme schemes for an nn-line poem is given by the Bell numbers. For example, B_3 = 5B3​=5, it means there are five rhyme schemes for a three-line poem: AAA, AAB, ABA, ABB, and ABC.

The question is to output the kk-th rhyme scheme in alphabetical order for a poem of nn lines.For example: the first rhyme scheme of a three-line poem is "AAA'', the fourth rhyme scheme of a three-line poem is ABB''.

InputFile

The first line of the input gives the number of test cases, TT (1 \leq T \leq 100001≤T≤10000). TT test cases follow.

Each test case contains a line with two integers nn and kk.

1 \leq n \leq 26, 1 \leq k \leq B_n1≤n≤26,1≤k≤Bn​ (B_nBn​ is the nn-th of Bell numbers)

OutputFile

For each test case, output one line containing Case #x: y, where xx is the test case number (starting from 11) and yy is the rhyme scheme contains uppercase letters.

樣例輸入複製

7
1 1
2 1
3 1
3 2
3 3
3 4
3 5

樣例輸出複製

Case #1: A
Case #2: AA
Case #3: AAA
Case #4: AAB
Case #5: ABA
Case #6: ABB
Case #7: ABC

編輯代碼

 

#include <bits/stdc++.h>

using namespace std;
typedef long long ll;
const int mod = 1000000007;
const int maxn = 305;

int T, n;
__int128 k;
__int128 dp[36][36];
int res[maxn];

inline __int128 read() {
    __int128 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;
}


inline __int128 dfs1(int id, int limit) {
    if (id == n + 1)return 1;
    if (~dp[id][limit])
        return dp[id][limit];
    __int128 tot = 0;
    for (register int i = 0; i <= limit; ++i) {
        tot += dfs1(id + 1, max(limit, i + 1));
    }
    return dp[id][limit] = tot;
}

inline void solve(int id, int limit, __int128 leave) {
    if (id == n + 1) {
        for (register int i = 1; i <= n; ++i) {
            printf("%c", res[i] + 'A');
        }
        printf("\n");
        return;
    }
    for (register int i = 0; i <= limit; ++i) {
        __int128 cur = max(limit, i + 1);
        if (dp[id + 1][cur] >= leave) {
            res[id] = i;
            solve(id + 1, cur, leave);
            break;
        } else {
            leave -= dp[id + 1][cur];
        }
    }
}

int Case;

int main() {
#ifndef ONLINE_JUDGE
    //freopen("1.txt", "r", stdin);
#endif
    scanf("%d", &T);
    while (T--) {
        scanf("%d%lld", &n,&k);
        //k = read();
        for (register int i = 0; i <= 30; ++i) {
            for (register int j = 0; j <= 30; ++j) {
                dp[i][j] = -1;
            }
        }
        for (register int i = 0; i <= 30; ++i)dp[n + 1][i] = 1;
        dfs1(1, 0);
        printf("Case #%d: ", ++Case);
        solve(1, 0, k);
    }
    return 0;
}