#include<bits/stdc++.h>
#define poly vector<int>
#define IOS ios::sync_with_stdio(false)
#define ll long long
#define mp make_pair
#define mt make_tuple
#define pa pair < int,int >
#define fi first
#define se second
#define inf 1e18
#define mod 998244353
#define sz(x) (int)((x).size())
#define int ll
//#define N
using namespace std;
bool f[5005][5005];
int du[5005];
int n;
mt19937_64 rnd(time(0));
int m;
inline int calcc()
{
	int tot=0;
	for (int x=0;x<n;x++)
		for (int y=x+1;y<n;y++)
			for (int k=y+1;k<n;k++)
				if (f[x][y]&&f[y][k]&&f[k][x]
				||f[y][x]&&f[k][y]&&f[x][k]) tot++;
	return tot;
}
inline int C(int x)
{
	return x*(x-1)/2;
}
inline int calc()
{
	int tot=n*(n-1)*(n-2)/6;
	for (int i=0;i<n;i++)
	{
		tot-=C(du[i]);
	}
	return tot;
}
poly G[5005];
inline int calc(int x,int y)
{
	if (y==0) return 0;
	return C(x/y)*(y-x%y)+(x%y)*C(x/y+1);
}
void BellaKira()
{
	cin>>n;
	int tot=0;
	if (n%2==1) tot=(n+1)*n*(n-1)/24;
	else tot=(n+2)*n*(n-2)/24;
	cin>>m;
	if (m>tot)
	{
		cout<<"No\n";
		return;
	}
	// for (int d=1;d<(n+1)/2;d++)
		// for (int i=0;i<n;i++)
		// {
			// f[i][(i+d)%n]=1;
		// }
	// if (n%2==0)
	// {
		// for (int i=0;i<n/2;i++)
			// f[i][(i+n/2)%n]=1;
	// }
	// for (int i=0;i<n;i++)
	// {
		// du[i]=0;
		// for (int j=0;j<n;j++)
			// if (f[i][j]) du[i]++;
	// }
	int sm=0,sx=0;
	for (int i=0;i<n;i++)
	{
		du[i]=0;
		int l=i*(i+1)/2-sm;
		if (i) l=max(l,du[i-1]);
		int r=(n*(n-1)/2-sm)/(n-i);
		int mn=r;
		for (int j=l;j<=r;j++)
		{
			// cout<<"!"<<i<<" "<<j<<" "<<
			// sm+j*(n-i)<<" "<<
			// n*(n-1)*(n-2)/6-(sx+C(j)+calc(n*(n-1)/2-sm-j,n-i-1))
			// <<" "<<calc(n*(n-1)/2-sm-j,n-i-1)<<endl;
			if (sm+j*(n-i)<=n*(n-1)/2&&
			n*(n-1)*(n-2)/6-(sx+C(j)+calc(n*(n-1)/2-sm-j,n-i-1))
			>=m)
			{
				mn=j;
				break;
			}
		}
		// cout<<"chos "<<i<<" "<<mn<<" from "<<l<<" "<<r<<endl;
		du[i]=mn;
		sm+=du[i];
		sx+=C(du[i]);
	}
	// return;
	// cout<<sm<<" "<<n*(n-1)/2<<" "<<n*(n-1)*(n-2)/6-sx<<endl;
	// cout<<calc()<<" "<<m<<'\n';
	// return;
	// for (int i=0;i<n;i++) cout<<du[i]<<" ";
	// cout<<'\n';
	vector<pa>all;
	for (int i=0;i<n;i++) all.push_back(mp(du[i],i));
	for (int i=0;i+1<n;i++)
	{
		sort(all.begin(),all.end());
		int c=n-i-all[0].fi-1;
		for (int j=1;j<=c;j++)
		{
			all[n-i-j].fi--;
			f[all[n-i-j].se][all[0].se]=1;
		}
		for (int k=1;k<n-i-c;k++)
			f[all[0].se][all[k].se]=1;
		reverse(all.begin(),all.end());
		all.pop_back();
		reverse(all.begin(),all.end());
	}
	// return;
	cout<<"Yes\n";
	for (int i=1;i<n;i++)
	{
		for (int j=0;j<i;j++) 
			cout<<f[i][j];
		cout<<'\n';
	}
	// cout<<calcc()<<endl;
	for (int i=0;i<n;i++)
		for (int j=0;j<n;j++) f[i][j]=0;
}
signed main()
{
	IOS;
	cin.tie(0);
	int T=1;
	cin>>T;
	while (T--)
	{
		BellaKira();
	}
}