#include <bits/stdc++.h>

using namespace std;

const int N = 5005;

int deg[N], o[N];
bitset<N> G[N];

int cmp(int x, int y) {
    return (deg[x] > deg[y]);
}

void output(int n) {
    puts("Yes");
    for (int i = 1; i <= n; ++i) {
        iota(o + i + 1, o + n + 1, i + 1);
        sort(o + i + 1, o + n + 1, cmp);
        for (int j = i + 1; j <= n; ++j) {
            G[o[j]][i] = (j <= n - deg[i]);
            deg[o[j]] -= G[o[j]][i];
        }
    }
    for (int i = 2; i <= n; ++i) {
        for (int j = 1; j < i; ++j) putchar(G[i][j] + '0');
        puts("");
    }
}

signed main() {
    int T; scanf("%d", &T);
    while (T--) {
        int n;
        long long m;
        scanf("%d%lld", &n, &m);
        int fl = 0;
        for (int tn = 1; tn <= n; ++tn) {
            long long S = 0;
            for (int i = 1; i <= tn; ++i) {
                deg[i] = (tn - 1) / 2 + ((tn & 1) ? 0 : (i > tn / 2));
                S += deg[i] * (deg[i] - 1ll) / 2;
            }
            if (S > tn * (tn - 1ll) * (tn - 2) / 6 - m) continue;
            int ts = (tn * (tn - 1ll) * (tn - 2) / 6 - m) - S;
            while (ts) {
                for (int i = 1; i <= tn && ts; ++i) {
                    int j = upper_bound(deg + 1, deg + tn + 1, deg[i]) - deg - 1;
                    if (deg[i] && j != i && deg[j] == deg[i]) {
                        --deg[i], ++deg[j], --ts;
                    }
                }
            }
            for (int i = tn + 1; i <= n; ++i) {
                deg[i] = i - 1;
            }
            fl = 1;
            output(n);
            break;
        }
        if (!fl) puts("No");
    }
    return 0;
}