B.K-th Beautiful String

Find the law

Can be found in the first position is a b x, a second position b in the last, it is the lexicographic order $ x * (x-1) / 2 $

Thus solving equations $ x * (x-1) / 2 = n $

#include<iostream>
#include<cmath>
using namespace std;
typedef long long ll;
int main()
{
    int t; cin >> t;
    while (t--)
    {
        ll n;
        ll k; cin >> n >> k;
        ll x = (1 + sqrt(1 + 8 * k)) / 2;
        ll y = k - x * (x - 1) / 2;
        if (y) ++x;
        else y = x-1;
        for (ll i = 1; i <= n; ++i)
        {
            if (i == n-x+1) cout << "b";
            else if (i == n-y+1) cout << "b";
            else cout << "a";
        }
        puts("");
    }
    
    return 0;
}