#include <bits/stdc++.h>
using namespace std;
#define int long long
const int INF = 1e12;
int comb2(int x)
{
return x * (x-1) / 2;
}
int n,m;
bool verif(vector<int> v)
{
int pref = 0;
for(int i=1;i<=n;i++)
{
if(i > 1 && v[i-1] > v[i])
return 0;
pref += v[i];
if(pref < comb2(i))
return 0;
}
if(pref != comb2(n))
return 0;
return 1;
}
int calc(vector<int> v)
{
int tot = 0;
for(int i=1;i<=n;i++)
tot += comb2(v[i]);
return tot;
}
bool done;
vector<int> sol;
int fr[5005];
void recursiv(vector<int> newv)
{
for(int i=0;i<=n;i++)
fr[i]=0;
for(int i=1;i<=n;i++)
fr[newv[i]]++;
int mycalc = calc(newv);
int minfr = 0, maxfr = n;
while(fr[minfr] == 0)
minfr++;
while(fr[maxfr] == 0)
maxfr--;
while(1)
{
if(mycalc == m)
{
sol.clear();
sol.push_back(0);
for(int i=0;i<=n;i++)
for(int j=1;j<=fr[i];j++)
sol.push_back(i);
done = 1;
return;
}
assert(minfr <= maxfr);
if(minfr + 1 < maxfr)
{
int newcalc = mycalc - maxfr + 1 + minfr;
if(newcalc >= m)
{
fr[maxfr]--;
fr[maxfr - 1]++;
if(fr[maxfr] == 0)
maxfr--;
fr[minfr]--;
fr[minfr + 1]++;
if(fr[minfr] == 0)
minfr++;
mycalc = newcalc;
continue;
}
}
int closest = abs(mycalc - m), c_i, c_j, c_calc = -1;
for(int idk=n-1;idk>=2;idk--)
{
for(int i=0;i+idk<=n-1;i++)
{
int j = i+idk;
if(fr[i] > 0 && fr[j] > 0)
{
int newcalc = mycalc - j + 1 + i;
int newdist = abs(m - newcalc);
if(newdist < closest)
{
closest = newdist;
c_i = i;
c_j = j;
c_calc = newcalc;
}
}
}
}
if(c_calc == -1)
return;
mycalc = c_calc;
fr[c_i]--;
fr[c_i + 1]++;
fr[c_j]--;
fr[c_j - 1]++;
minfr = 0, maxfr = n;
while(fr[minfr] == 0)
minfr++;
while(fr[maxfr] == 0)
maxfr--;
}
}
int mat[5005][5005];
void reconstruct(vector<int> v)
{
assert(verif(v));
for(int i=1;i<=n;i++)
for(int j=1;j<=n;j++)
mat[i][j] = 0;
vector<pair<int,int>> aux;
for(int i=1;i<=n;i++)
aux.push_back({v[i], i});
while(!aux.empty())
{
sort(aux.begin(), aux.end());
if(aux.back().first == 0)
break;
assert(aux.back().first > 0);
for(int i=0;i<aux.back().first;i++)
{
mat[aux.back().second][aux[i].second] = 1;
}
for(int i=aux.back().first;i<(int)aux.size()-1;i++)
{
aux[i].first--;
mat[aux[i].second][aux.back().second] = 1;
}
aux.back().first = 0;
aux.pop_back();
}
for(int i=1;i<=n;i++)
{
for(int j=i+1;j<=n;j++)
{
assert(mat[i][j] + mat[j][i] == 1);
if(mat[i][j] + mat[j][i] != 1)
{
//cerr<<i<<" "<<j<<": "<<mat[i][j]<<" & "<<mat[j][i]<<" zzz\n";
}
}
}
for(int i=2;i<=n;i++)
{
for(int j=1;j<i;j++)
cout<<mat[i][j];
cout<<"\n";
}
}
void solve()
{
cin>>n>>m;
m = n * (n-1) * (n-2) / 6 - m;
//get close to m then do backtrack
done = 0;
vector<int> init(n+2,0);
for(int i=1;i<=n;i++)
init[i] = i - 1;
assert(verif(init));
if(m > calc(init))
{
cout<<"No\n";
return;
}
recursiv(init);
if(!done)
{
cout<<"No\n";
return;
}
assert(calc(sol) == m);
//for(int i=1;i<=n;i++) cerr<<sol[i]<<" ";cerr<<"sol\n";
cout<<"Yes\n";
reconstruct(sol);
}
signed main()
{
ios_base::sync_with_stdio(0);cin.tie(0);
int t;
cin>>t;
while(t--)
solve();
return 0;
}
/*
for each "bad" tuple (x,y,z) of nodes,
exactly one of x,y,z will have outgoing edges towards the other 2
=> M = total - sum(comb(cnt_outgoing(x), 2))
*/
