#include <bits/stdc++.h>
using namespace std;
using ll = long long; using pii = pair<ll,ll>;
vector<vector<bool>> ans;
void prc(vector<pii> v0) { //has this outdegree
if (v0.size()<=1) {
return;
}
//sort(v0.begin(),v0.end());
vector<pii> v1,v2,v3;
pii pbk = v0.back();
ll szl = v0.size()-1;
ll num1 = pbk.first;
ll x0 = pbk.second;
ll DMAX = -1;
for (ll i=0;i<num1;i++) {
ll xc = v0[i].second; ll cdeg = v0[i].first;
ans[x0][xc]=1;
ans[xc][x0]=0;
v1.push_back({cdeg,xc});
DMAX = cdeg;
}
for (ll i=num1;i<szl;i++) {
ll xc = v0[i].second; ll cdeg = v0[i].first;
ans[x0][xc]=0;
ans[xc][x0]=1;
if (cdeg==DMAX) {
v3.push_back({cdeg-1,xc});
} else {
v2.push_back({cdeg-1,xc});
}
}
vector<pii> vf;
for (pii p0: v1) {
if (p0.first!=DMAX) {
vf.push_back(p0);
}
}
for (pii p0: v3) {
vf.push_back(p0);
}
for (pii p0: v1) {
if (p0.first==DMAX) {
vf.push_back(p0);
}
}
for (pii p0: v2) {
vf.push_back(p0);
}
prc(vf);
}
void solve(ll N, ll M) {
ans.clear();
ll Mmax = (N*(N-1)*(N-2))/6;
// ll flr = (N-1)/2;
// Mmax -= N*(flr*(flr-1))/2;
if (N%2==0) {
Mmax-=(N/2)*((N/2)*(N/2-1))/2;
Mmax-=(N/2)*((N/2-2)*(N/2-1))/2;
} else {
Mmax-=N*((N/2)*(N/2-1))/2;
}
//cout << "M,Mmax="<<M<<","<<Mmax<<"\n";
// exit(0);
if (M>Mmax) {
cout << "No\n";
return;
}
if (N==3) {
cout << "Yes\n";
if (M==1) {
cout << "0\n10\n";
} else {
cout << "0\n01\n";
}
return;
}
if (N==4) {
cout << "Yes\n";
if (M==0) {
cout << "0\n01\n010\n";
} else if (M==1) {
cout << "0\n10\n111\n";
} else if (M==2) {
cout << "0\n01\n100\n";
}
return;
}
if (N%2==0) {
cout << "Yes\n";
vector<ll> vdegs;
ll ndel = Mmax-M; //# to delete
ll npl = N/2; //# of pairs left
ll JMAX = N/2-1;
while (npl>0) {
assert(ndel>=0);
//cout << "npl="<<npl<<"\n";
//cout << "ndel="<<ndel<<"\n";
if (ndel==0) {
//cout << "0blk\n";
vdegs.push_back(N/2);
vdegs.push_back((N/2)-1);
npl--;
} else if (ndel==5) {
//cout << "5blk\n";
vdegs.push_back((N/2)-2);
vdegs.push_back((N/2)-2);
vdegs.push_back((N/2));
vdegs.push_back((N/2)+2);
npl-=2;
ndel-=5;
} else if (ndel==1) {
assert(npl>=2);
//cout << "1blk\n";
vdegs.push_back((N/2)-1);
vdegs.push_back((N/2)-1);
vdegs.push_back((N/2)-1);
vdegs.push_back((N/2)+1);
npl-=2;
ndel-=1;
} else {
while (ndel<(JMAX*(JMAX+1))) {
JMAX--;
}
npl-=1;
ndel-=(JMAX*(JMAX+1));
//cout << "jblk,val="<<(JMAX*(JMAX+1))<<"\n";
vdegs.push_back((N/2)+JMAX);
vdegs.push_back((N/2)-1-JMAX);
if (JMAX>2) {
JMAX--;
}
}
}
//exit(0);
assert(npl==0);
vector<pii> vdegQ;
vector<bool> vbk(N,false);
for (ll i=0;i<N;i++) {
ans.push_back(vbk);
vdegQ.push_back({vdegs[i],i});
//cout << "vdegQ term: "<<vdegs[i]<<","<<i<<"\n";
}
//exit(0);
sort(vdegQ.begin(),vdegQ.end());
prc(vdegQ);
for (ll i=1;i<N;i++) {
for (ll j=0;j<i;j++) {
cout << ans[i][j];
}
cout << "\n";
}
} else {
cout << "Yes\n";
vector<ll> vdegs;
ll ndel = Mmax-M;
ll nel = N; //# of elements left
ll JMAX = (N-1)/2;
//cout << "ndel,nel="<<ndel<<","<<nel<<"\n"; exit(0);
while (nel>0) {
assert(ndel>=0);
if (ndel==0) {
vdegs.push_back((N-1)/2);
nel--;
} else if (ndel==3) {
vdegs.push_back((N-1)/2+1);
vdegs.push_back((N-1)/2+1);
vdegs.push_back((N-1)/2-2);
nel-=3;
ndel-=3;
} else {
while (ndel<(JMAX*JMAX)) {
JMAX--;
}
ndel-=JMAX*JMAX;
nel-=2;
vdegs.push_back((N-1)/2+JMAX);
vdegs.push_back((N-1)/2-JMAX);
if (JMAX>2) {
JMAX--;
}
}
}
assert(nel==0);
vector<pii> vdegQ;
vector<bool> vbk(N,false);
for (ll i=0;i<N;i++) {
ans.push_back(vbk);
vdegQ.push_back({vdegs[i],i});
//cout << "pair: "<<vdegs[i]<<","<<i<<"\n";
}
//exit(0);
sort(vdegQ.begin(),vdegQ.end());
prc(vdegQ);
for (ll i=1;i<N;i++) {
for (ll j=0;j<i;j++) {
cout << ans[i][j];
}
cout << "\n";
}
}
}
int main() {
ios_base::sync_with_stdio(false); cin.tie(0);
ll Q; cin >> Q;
while (Q--) {
ll N,M; cin >> N >> M;
solve(N,M);
}
}
