Bittilista

#include <iostream>
using namespace std;
typedef long long ll;
ll dp[51][2][51][51];
int main() {
    ll n,k;
    cin>>n>>k;
    dp[1][0][0][0] = 1;
    dp[1][1][0][0] = 1;
    for(int i = 2; i <= n; ++i) {
        for(int io = 0; io < n; ++io) {
            for(int oi = 0; oi < n; ++oi) {
                dp[i][1][io+1][oi] += dp[i-1][0][io][oi];
                dp[i][1][io][oi] += dp[i-1][1][io][oi];
                dp[i][0][io][oi+1] += dp[i-1][1][io][oi];
                dp[i][0][io][oi] += dp[i-1][0][io][oi];
            }
        }
    }
    int ed = 2;
    int io = 0;
    int oi = 0;
    for(int i = n; i >= 1; --i) {
        ll sum0 = 0;
        if(ed == 1) ++io;
        for(int j = 0; j < n; ++j) {
            if(j - io >= 0 && j - oi >= 0)
            sum0 += dp[i][0][j-io][j-oi];
        }
        if(ed == 1) --io;
        //cout<<sum0<<'\n';
        if(sum0 >= k) {
            if(ed == 1) ++io;
            ed = 0;
            cout<<0;
        }
        else {
            if(ed == 0) ++oi;
            ed = 1;
            k -= sum0;
            cout<<1;
        }
    }
    cout<<'\n';

}

Test 1

Group: 1

Verdict: ACCEPTED

Test 2

Group: 1

Verdict: ACCEPTED

Test 3

Group: 1

Verdict: ACCEPTED

Test 4

Group: 1

Verdict: ACCEPTED

Test 5

Group: 1

Verdict: ACCEPTED

Test 6

Group: 2

Verdict: ACCEPTED

Test 7

Group: 2

Verdict: ACCEPTED

Test 8

Group: 2

Verdict: ACCEPTED

Test 9

Group: 2

Verdict: ACCEPTED

Test 10

Group: 2

Verdict: ACCEPTED

Test 11

Group: 3

Verdict: ACCEPTED

Test 12

Group: 3

Verdict: ACCEPTED

Test 13

Group: 3

Verdict: ACCEPTED

Test 14

Group: 3

Verdict: ACCEPTED

Test 15

Group: 3

Verdict: ACCEPTED