#include <bits/stdc++.h>
using namespace std;
#define int long long
int f(int n) {
int res = 0, h = n / 2;
// h, n-1-h
for (int i = 1; i <= n; i++) {
res += h * (h - 1) / 2;
res += (n - h - 2) * (n - h - 1) / 2;
}
// cout << "res " << n << " " << res << '\n';
return n * (n - 1) * (n - 2) / 6 - (res / 2);
}
vector<vector<int>> comp(int n, int x) {
vector<vector<int>> g(n+1, vector<int> (n+1, -1));
auto norm = [&] (int i) {
if (i > n) return i - n;
return i;
};
auto ae = [&] (int a, int b) {
if (a < b) g[b][a] = 1;
else g[a][b] = 0;
};
vector<int> d(n+1, 0);
vector<set<int>> val(n+1);
set<int> cand;
for (int i = 1; i <= n; i++) {
int t = n/2, x = norm(i+1);
if (n % 2 == 0 && i > n/2) t--;
while (t--) {
ae(i, x);
d[x]++;
x = norm(x+1);
}
}
for (int i = 1; i <= n; i++) val[d[i]].insert(i);
for (int i = 1; i <= n; i++) if (val[i].size() >= 2) cand.insert(i);
int times = f(n) - x;
for (int i = 0; i < times; i++) {
// cout << times << ' ' << i << '\n';
assert(!cand.empty());
int tp = *cand.begin();
cand.erase(tp);
if (!tp) tp = *cand.begin();
cand.erase(tp);
assert(val[tp].size() >= 2);
int f = *val[tp].begin(); val[tp].erase(f);
int s = *val[tp].begin(); val[tp].erase(s);
if (g[f][s]) d[f]--, d[s]++;
else d[f]++, d[s]--;
g[f][s] ^= 1;
val[d[f]].insert(f);
val[d[s]].insert(s);
cand.erase(d[f]); cand.erase(d[s]);
if (val[d[f]].size() >= 2) cand.insert(d[f]);
if (val[d[s]].size() >= 2) cand.insert(d[s]);
if (val[tp].size() >= 2) cand.insert(tp);
}
// for (int i = 2; i <= n; i++) {
// for (int j = 1; j < i; j++) cout << g[i][j];
// cout << '\n';
// }
return g;
}
void solve() {
int n, m, np = -1;
cin >> n >> m;
for (int i = 1;; i++) {
// cout << i << " " << f(i) << "\n";
if (f(i) >= m) {
np = i;
break;
}
}
if (np > n || np == -1) return cout << "No\n", void();
vector<vector<int>> g = comp(np, m);
// 1 <=> larger wins
cout << "Yes\n";
for (int i = 2; i <= n; i++) {
for (int j = 1; j < i; j++) {
if (i > np || j > np) g[i][j] = 1;
cout << g[i][j];
}
cout << '\n';
}
}
int32_t main() {
ios::sync_with_stdio(0); cin.tie(0);
int q;
cin >> q;
while (q--) solve();
}
