#include <iostream>
#include <vector>
#include <set>
#include<algorithm>
#include<queue>
#include<map>
#include<math.h>
#include<assert.h>
#include<random>
#define ll long long
#define int ll
#define i32 __int32_t
#define i64 __int64_t
#define i128 __int128_t
#define db double
#define pii pair<int,int>
#define pll pair<ll,ll>
#define bk back()
#define bg begin()
#define ed end()
#define vi vector<int>
#define vii vector<pii>
#define rep(i,a,b) for(int i=(a); i<=(b); i++)
#define all(x) (x).begin(), (x).end()
#pragma GCC optimize("Ofast,unroll-loops,no-stack-protector,fast-math")
#pragma GCC target("avx,avx2,fma")
using namespace std;
int N,M;
int F(int k, int n){
return (k/n)*(k/n+1)/2 * (k%n) + (k/n)*(k/n-1)/2 * (n-k%n);
}
int a[5050];
pii v[5050];
bool ans[5050][5050];
void solve(){
cin>>N>>M;
M= N*(N-1)*(N-2)/6 - M;
int k=N*(N-1)/2;
if(F(k, N)>M){
cout<<"No\n";
return;
}
a[N+1]=N-1;
for(int i=N; i>1; i--){
a[i] = a[i+1];
for(; a[i]>=0; a[i]--){
if(F(k-a[i], i-1) + a[i]*(a[i]-1)/2 <= M && (k-a[i])>=(i-2)*(i-1)/2){
break;
}
}
k -= a[i];
M -= a[i]*(a[i]-1)/2;
}
a[1]=k;
k-=a[1];
M-=a[1]*(a[1]-1)/2;
for(int i=1; i<=N; i++) v[i] = {a[i],i};
rep(i,1,N) rep(j,1,N) ans[i][j]=0;
for(int i=N; i>0; i--){
for(int j=1; j<=v[i].first; j++){
ans[v[j].second][v[i].second]=1^(v[i].second<v[j].second);
ans[v[i].second][v[j].second]=1^(v[i].second<v[j].second);
}
for(int j=v[i].first+1; j<i ;j++){
ans[v[j].second][v[i].second]=(v[i].second<v[j].second);
ans[v[i].second][v[j].second]=(v[i].second<v[j].second);
v[j].first--;
}
sort(v+1, v+i);
}
cout<<"Yes\n";
for(int i=2; i<=N; i++){
for(int j=1; j<i; j++) cout<<ans[i][j];
cout<<"\n";
}
}
signed main(){
ios_base::sync_with_stdio(0);cin.tie(0);
int tc;cin>>tc;while(tc--)solve();
}
