#include <bits/stdc++.h>
using namespace std;
#define F0R(i, n) for (int i = 0; i < n;i++)
#define FOR(i,j, n) for (int i = j; i < n;i++)
template<typename T>
using V = vector<T>;
using vi = V<int>;
vi dp;
V<V<bool>> g;
void connect(int l, int r, int l2, int r2) {
FOR(i, l, r) {
FOR(j, l2, r2) {
g[i][j] = 1;
g[j][i] = 0;
}
}
}
void solve(int startI, int N, int k) {
if (k == 0) return;
FOR(j, 1, N) {
if (dp[j] + dp[N - j] >= k) {
// Do this
solve(startI, j,min(dp[j], k));
solve(startI + j, N - j, k - min(dp[j], k));
connect(startI + j, startI + N,startI, startI + j);
return;
}
}
FOR(j, 1, N) {
FOR(t, 1, N) {
if (j + t >= N) continue;
if (dp[t] + dp[j] + dp[N - j - t] + j * t * (N - j - t) >= k and j * t * (N - j - t) <= k) {
// Split 3
k -= j * t * (N - j - t);
solve(startI, j, min(k, dp[j]));
solve(startI + j, t, min(k - min(k, dp[j]), dp[t]));
solve(startI + j + t, N - j - t, k - min(k - min(k, dp[j]), dp[t]));
connect(startI + j + t, startI + N,startI + j, startI + j + t); //
connect(startI + j, startI + j + t,startI, startI + j); //
connect(startI, startI + j,startI + j + t, startI + N); //
return;
}
}
}
exit(5);
}
int main() {
ios_base::sync_with_stdio(false); cin.tie(nullptr);
int q; cin >> q;
F0R(test, q) {
int n, K; cin >> n >> K;
dp.clear();
dp.resize(n + 1);
FOR(i, 1, n + 1) {
F0R(j, i) {
dp[i] = max(dp[i], dp[j] + dp[i - j]);
}
FOR(j, 1, i) {
FOR(k, 1, i) {
if (j + k >= i) continue;
dp[i] = max(dp[i], dp[k] + dp[j] + dp[i - j - k] + j * k * (i - j - k));
}
}
}
g.clear();
g.resize(n,V<bool>(n));
if (dp[n] >= K) {
cout << "YES\n";
solve(0, n, K);
F0R(i,n) {
F0R(j, n) {
if (i <= j) continue;
cout << (g[i][j] ? '1': '0') << "";
}
cout << "\n";
}
} else {
cout << "NO\n";
}
}
return 0;
}
