Pascal Walk AC solution

#include <bits/stdc++.h>
#define int long long
#define uint unsigned long long
#define double long double
#pragma GCC optimize("O3,Ofast,no-stack-protector,fast-math,unroll-loops")
using namespace std;

int pasc[501][501];

void init() {
    pasc[1][1] = 1;
    for (int i = 2; i <= 500; i++) {
        pasc[i][1] = 1;
        pasc[i][i] = 1;
        for (int j = 2; j < i; j++) {
            pasc[i][j] = pasc[i - 1][j - 1] + pasc[i - 1][j];
            pasc[i][j] %= 1000000000000;
        }
    }
}

bool solve(int i, int n, int z, bool show) {
    int x = 0;
    int q = 0;
    int r = 1;
    int k = 1;
    if (show) {
        cout << "Case #" << i << ":\n";
    }
    while (x < n) {
        q++;
        x += pasc[r][k];
        if (show) {
            cout << r << ' ' << k << '\n';
        }
        if (r < z) {
            r++;
        } else {
            bool cond;
            if (r == k) {
                cond = (x + pasc[r + 1][k + 1] <= n);
            } else {
                cond = (x + pasc[r + 1][k + 1] <= n);
            }
            if (cond) {
                r++;
                k++;
            } else {
                k++;
            }
        }
    }
    return q <= 499 && x == n;
}

signed main() {
    init();
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);

    int t;
    cin >> t;
    for (int i = 1; i <= t; i++) {
        int n;
        cin >> n;
        for (int z = 16; z >= 1; z--) {
            if (solve(i, n, z, 0)) {
                solve(i, n, z, 1);
                break;
            }
        }
    }

    fflush(stdout);
    return 0;
}