#include "bits/stdc++.h" /** keep-include */
using namespace std;
#define rep(i, b, e) for(int i = (b); i <= (e); i++)
#define per(i, b, e) for(int i = (e); i >= (b); i--)
#define FOR(i, b, e) rep(i, b, (e) - 1)
#define SZ(x) int(x.size())
#define all(x) x.begin(), x.end()
#define pb push_back
#define mp make_pair
#define st first
#define nd second
using ll = long long;
using vi = vector<int>;
using pii = pair<int, int>;
auto &operator<<(auto &o, pair<auto, auto> p) {
return o << "(" << p.st << ", " << p.nd << ")"; }
auto operator<<(auto &o, auto x)->decltype(end(x), o) {
o << "{"; int i=0; for(auto e: x) o << ", " + 2*!i++ << e;
return o << "}"; }
#ifdef LOCAL
#define deb(x...) cerr << "[" #x "]: ", [](auto...$) { \
((cerr << $ << "; "),...) << endl; }(x)
#else
#define deb(...)
#endif
vector<vector<int> > get_tournament(vector<int> V){
deb(V);
int n=V.size();
if(n==1){
assert(V==vi({0}));
return {{0}};
}
int d=n-1-V.back();
V.pop_back();
vi decreased;
vi cur;
for(int i=n-2; ; i--){
if(i!=n-2 && (i==-1 || V[i]!=V[i+1])){
while(d && cur.size()){
assert(V[cur.back()]);
V[cur.back()]--;
decreased.pb(cur.back());
cur.pop_back();
d--;
}
cur.clear();
}
if(i==-1)break;
cur.pb(i);
}
auto res=get_tournament(V);
res.pb(vi(n-1, 1));
for(int i=0; i<n-1; i++){
res[i].pb(0);
}
for(int i:decreased){
res[i][n-1]=1;
res[n-1][i]=0;
}
return res;
}
vector<int> degrees;
bool backtrack(int n, int sum_deg, int sum_deg2, int max_deg){
deb(n, sum_deg, sum_deg2, max_deg);
//if(sum_deg2>n*max_deg*max_deg)return false;
//if(sum_deg2<(sum_deg*sum_deg)/n)return false;
if(n==1){
if(sum_deg2==sum_deg*sum_deg && sum_deg<=max_deg){
degrees.pb(sum_deg);
return 1;
}
else return 0;
}
for(int deg=max_deg; deg>=0; deg--){
if(sum_deg-deg<(n-2)*(n-1)/2)break;
if(deg*n<sum_deg)break;
degrees.pb(deg);
if(backtrack(n-1, sum_deg-deg, sum_deg2-deg*deg, deg))return true;
degrees.pop_back();
}
return false;
}
//pamietac o tym ze m long longiem gdy n >=2000
void solve() {
int n, m;
cin>>n>>m;
int sum_deg=n*(n-1)/2;
int sum_deg2=2*(sum_deg*(n-2)/3-m)+sum_deg;
deb(sum_deg, sum_deg2);
if(!backtrack(n, sum_deg, sum_deg2, n-1)){
cout<<"No\n";
return;
}
cout<<"Yes\n";
reverse(all(degrees));
auto res=get_tournament(degrees);
degrees.clear();
for(int i=1; i<n; i++){
for(int j=0; j<i; j++)cout<<res[i][j];
cout<<"\n";
}
}
int main() {
cin.tie(0)->sync_with_stdio(0);
int tt = 1;
cin >> tt;
FOR(te, 0, tt) solve();
return 0;
}
