//Author: Kevin
#include<bits/stdc++.h>
//#pragma GCC optimize("O2")
using namespace std;
#define ll long long
#define ull unsigned ll
#define pb emplace_back
#define mp make_pair
#define ALL(x) (x).begin(),(x).end()
#define rALL(x) (x).rbegin(),(x).rend()
#define srt(x) sort(ALL(x))
#define rev(x) reverse(ALL(x))
#define rsrt(x) sort(rALL(x))
#define sz(x) (int)(x.size())
#define inf 0x3f3f3f3f
#define pii pair<int,int>
#define lb(v,x) (int)(lower_bound(ALL(v),x)-v.begin())
#define ub(v,x) (int)(upper_bound(ALL(v),x)-v.begin())
#define uni(v) v.resize(unique(ALL(v))-v.begin())
#define longer __int128_t
void die(string S){puts(S.c_str());exit(0);}
int d[5005];
bool E[5005][5005];
int main()
{
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
	int t;
	cin>>t;
	while(t--)
	{
		int n;
		ll m;
		cin>>n>>m;
		m=1ll*n*(n-1)*(n-2)/3-m-m+n*(n-1)/2;
		ll Lb=0,Rb=0;
		for(int i=0;i<n;i++)
			Rb+=i*i;
		if((n-1)%2)
			for(int i=0;i<n/2;i++)
			{
				Lb+=((n-1)/2)*((n-1)/2);
				Lb+=(n/2)*(n/2);
			}
		else
			Lb=1ll*n*(n-1)*(n-1)/4;
		if(m<Lb||m>Rb)
			cout<<"No\n";
		else
		{
			for(int i=1;i<=n;i++)
			{
				int sum=accumulate(d+1,d+i,0);
				int lim=i*(i-1)/2-sum;
				lim=max(lim,d[i-1]);
				ll ssum=0;
				for(int j=1;j<i;j++)
					ssum+=d[j]*d[j];
				int j;
				for(j=lim;sum+j*(n-i+1)<=n*(n-1)/2;j++)
				{
					ll Bound=0;
					int cursum=n*(n-1)/2-sum-j;
					for(int x=0;x<n-i;x++)
						if(cursum%(n-i)>x)
							Bound+=(cursum/(n-i)+1)*(cursum/(n-i)+1);
						else
							Bound+=(cursum/(n-i))*(cursum/(n-i));
					if(Bound+ssum+j*j<=m)
						break;
				}
				d[i]=j;
			}
			ll sm=0;
			for(int i=1;i<=n;i++)
				sm+=d[i]*d[i];
			assert(sm==m);
			cout<<"Yes\n";
			for(int i=0;i<=n;i++)
				for(int j=0;j<=n;j++)
					E[i][j]=0;
			vector<pii> vec;
			for(int i=0;i<n;i++)
				vec.pb(d[i+1],i);
			for(int i=0;i<n-1;i++)
			{
				srt(vec);
				int c=n-i-vec[0].first-1;
				for(int k=1;k<=c;k++)
				{
					vec[n-i-k].first--;
					E[vec[n-i-k].second][vec[0].second]=1;
				}
				for(int k=1;k<n-i-c;k++)
					E[vec[0].second][vec[k].second]=1;
				vec.erase(vec.begin());
			}
			for(int i=1;i<n;i++)
			{
				for(int j=0;j<i;j++)
					cout<<E[i][j];
				cout<<'\n';
			}
		}
	}
	return 0;
}