#include<bits/stdc++.h>

#define vc vector
#define pb emplace_back
#define pii pair<int, int>
#define mkp make_pair
#define rep(i, a, b) for(int i = (a); i <= (b); ++i)
#define lep(i, a, b) for(int i = (a); i >= (b); --i)

#define int long long

using namespace std;
bool st;

mt19937 gen(time(0));

inline int read() {
	int x = 0, w = 0; char ch = getchar(); while(!isdigit(ch)) w |= (ch == '-'), ch = getchar();
	while(isdigit(ch)) x = x * 10 + (ch ^ 48), ch = getchar(); return w ? -x : x; 
}

const int N = 5005;

int n, m, tot, buc[N], inq[N], deg[N];
bool a[N][N];
queue <int> Q;

inline int c3 (int n) { return n * (n - 1) * (n - 2) / 6; }
inline int c2 (int n) { return n * (n - 1) / 2; }

inline int calc (int m) {
	int res = c3 (m), Deg = c2 (m);
	rep (i, 1, m) deg[i] = Deg / m;
	rep (i, m + 1, n) deg[i] = i - 1;
	rep (i, 1, Deg % m) ++ deg[i];
	rep (i, 1, m) res -= c2 (deg[i]);
	return res;
}

inline void construct () {
	rep (i, m + 1, n) deg[i] = i - 1;
	for (int i = 0, j = 0; i < m; i ++) 
		while (buc[i]) deg[++ j] = i, -- buc[i];
	lep (i, n, 1) {
		int cnt = deg[i], val = deg[cnt], pos = i;
		rep (j, 1, i - 1) 
			if (deg[j] < val) -- cnt, a[i][j] = 1;
			else if (deg[j] > val) { pos = pos == i ? j : pos; -- deg[j]; }
		lep (j, pos - 1, 1) if (deg[j] == val) {
			if (cnt) -- cnt, a[i][j] = 1;
			else -- deg[j];
		}
	}
}

inline void testcase () {
	n = read (); tot = read (); 
	
	rep (i, 0, n) rep (j, 0, n) a[i][j] = 0;
	
	if (tot == 0) {
		puts ("Yes");
		rep (i, 2, n) {
			rep (j, 1, i - 1) printf("1");
			putchar (10);
		}
		return ;
	}
	
	rep (i, 0, n) buc[i] = 0, inq[i] = 0;
	while (!Q.empty ()) Q.pop ();
	
	m = 0;
	rep (i, 1, n) if (calc (i) >= tot) { m = i; break; }
	if (!m) return puts ("No"), void ();
	puts ("Yes");
	
	int avr = c2 (m) / m; tot = calc (m) - tot;
	buc [avr] = m - c2 (m) % m; Q.push (avr); inq[avr] = 1;
	buc [avr + 1] = c2 (m) % m; Q.push (avr + 1); inq[avr] = 1;
	
	while (tot) {
		int x = Q.front (); Q.pop (); inq[x] = 0;
		if (buc[x] < 2 || x == 0 || x == m - 1) { continue; }
		if (buc[x] > 3) Q.push (x), inq[x] = 1;
		-- tot; buc[x] -= 2; ++ buc[x - 1]; ++ buc[x + 1];
		if (buc[x - 1] == 2 && !inq[x - 1]) Q.push (x - 1), inq[x - 1] = 1;
		if (buc[x + 1] == 2 && !inq[x + 1]) Q.push (x + 1), inq[x + 1] = 1;
	}
	
	construct (); 
	
	rep (i, 2, n) {
		rep (j, 1, i - 1) printf ("%d", a[i][j]);
		putchar (10);
	}
}

bool ed;
signed main() {
	cerr << (&ed - &st) / 1024 / 1024 << "MB ---------------------------" << endl;
	
	int t = read (); while (t--) testcase (); 
	return 0;
}