#include<bits/stdc++.h>
using namespace std;
#define ll long long
// I love table tennis!
ll ans[5005];
ll id[5005],od[5005];
void solve(){
ll n,k;
cin>>n>>k;
if(ans[n]<k){
cout<<"No\n"; return;
}
if(k==0){
cout<<"Yes\n";
for(int i=1;i<=n-1;i++){
for(int j=1;j<=i;j++){
cout<<"1";
}
cout<<'\n';
}
return;
}
cout<<"Yes\n";
ll indeg[n+2],outdeg[n+2];
bool edge[n+2][n+2];
for(int i=0;i<n+2;i++){
indeg[i]=outdeg[i]=0;
}
ll rn;
for(int i=n;i>=2;i--){
if(ans[i]<k){rn=i+1; break;}
}
for(int i=1;i<=rn;i++){
if(i==1){
continue;
}
ll mx,mn;
for(int j=1;j<i;j++){
if(j==1)mx=indeg[j],mn=indeg[j];
else mx=max(mx,indeg[j]),mn=min(mn,indeg[j]);
}
if(mx==mn){
for(int j=1;j<=(i-1)/2;j++){indeg[j]++,outdeg[i]++; edge[i][j]=1; edge[j][i]=0;}
for(int j=(i-1)/2+1;j<i;j++){outdeg[j]++,indeg[i]++; edge[j][i]=1; edge[i][j]=0;}
}
else{
for(int j=1;j<i;j++){
if(indeg[j]==mn){indeg[j]++,outdeg[i]++; edge[i][j]=1; edge[j][i]=0;}
else{indeg[i]++,outdeg[j]++; edge[j][i]=1; edge[i][j]=0;}
}
}
}
set<ll>st;
vector<ll>degs[n+5];
for(int i=1;i<=rn;i++){
// cout<<id[i]<<" ";
degs[indeg[i]].push_back(i);
}
for(int i=1;i<=rn;i++){
if(degs[i].size()>=2){
st.insert(i);
}
}
ll diff=ans[rn]-k;
for(int i=1;i<=diff;i++){
ll lol=*st.begin();
ll cur1=degs[lol][degs[lol].size()-1]; degs[lol].pop_back();
ll cur2=degs[lol][degs[lol].size()-1]; degs[lol].pop_back();
if(degs[lol].size()<2){
st.erase(st.find(lol));
}
if(edge[cur1][cur2]){
edge[cur1][cur2]=0; edge[cur2][cur1]=1;
degs[lol+1].push_back(cur1);
degs[lol-1].push_back(cur2);
if(degs[lol+1].size()>=2)st.insert(lol+1);
if(degs[lol-1].size()>=2)st.insert(lol-1);
}
else{
edge[cur1][cur2]=1; edge[cur2][cur1]=0;
degs[lol+1].push_back(cur2);
degs[lol-1].push_back(cur1);
if(degs[lol+1].size()>=2)st.insert(lol+1);
if(degs[lol-1].size()>=2)st.insert(lol-1);
}
}
for(int i=1;i<=n;i++){
for(int j=1;j<=n;j++){
if(i==j)continue;
if(i<=rn&&j<=rn)continue;
else{
if(i<j)edge[i][j]=1;
else edge[i][j]=0;
}
}
}
for(int i=2;i<=n;i++){
for(int j=1;j<i;j++){
if(edge[i][j])cout<<1;
else cout<<0;
}
cout<<'\n';
}
}
int main(){
ios::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
for(int i=1;i<=5000;i++){
if(i==1)continue;
ll mx,mn;
for(int j=1;j<i;j++){
if(j==1)mx=id[j],mn=id[j];
else mx=max(mx,id[j]),mn=min(mn,id[j]);
}
if(mx==mn){
for(int j=1;j<=(i-1)/2;j++)id[j]++,od[i]++;
for(int j=(i-1)/2+1;j<i;j++)od[j]++,id[i]++;
}
else{
for(int j=1;j<i;j++){
if(id[j]==mn)id[j]++,od[i]++;
else id[i]++,od[j]++;
}
}
ll tot=0;
ans[i]=(ll)i*((ll)i-(ll)1)*((ll)i-(ll)2)/(ll)6;
for(int j=1;j<=i;j++){
tot+=(id[j]-1)*id[j]/2; tot+=(od[j]-1)*(od[j])/2;
}
ans[i]-=tot/2;
}
ll t;
cin>>t;
while(t--)solve();
}
