#include <iostream>

typedef long long ll;
typedef double lf;

// #define DEBUG 1
struct IO
{
    #define MAXSIZE (1 << 20)
    #define isdigit(x) (x >= '0' && x <= '9')
    char buf[MAXSIZE], *p1, *p2;
    char pbuf[MAXSIZE], *pp;
    #if DEBUG
    #else
    IO() : p1(buf), p2(buf), pp(pbuf) {}
    ~IO() {fwrite(pbuf, 1, pp - pbuf, stdout);}
    #endif
    #define gc() (p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, MAXSIZE, stdin), p1 == p2) ? ' ' : *p1++)
    #define blank(x) (x == ' ' || x == '\n' || x == '\r' || x == '\t')

    template <typename T>
    void Read(T &x)
    {
        #if DEBUG
        std::cin >> x;
        #else
        bool sign = 0; char ch = gc(); x = 0;
        for (; !isdigit(ch); ch = gc())
            if (ch == '-') sign = 1;
        for (; isdigit(ch); ch = gc()) x = x * 10 + (ch ^ 48);
        if (sign) x = -x;
        #endif
    }
    void Read(char *s)
    {
        #if DEBUG
        std::cin >> s;
        #else
        char ch = gc();
        for (; blank(ch); ch = gc());
        for (; !blank(ch); ch = gc()) *s++ = ch;
        *s = 0;
        #endif
    }
    void Read(char &c) {for (c = gc(); blank(c); c = gc());}

    void Push(const char &c)
    {
        #if DEBUG
        putchar(c);
        #else
        if (pp - pbuf == MAXSIZE) fwrite(pbuf, 1, MAXSIZE, stdout), pp = pbuf;
        *pp++ = c;
        #endif
    }
    template <typename T>
    void Write(T x)
    {
        if (x < 0) x = -x, Push('-');
        static T sta[35];
        int top = 0;
        do sta[top++] = x % 10, x /= 10; while (x);
        while (top) Push(sta[--top] ^ 48);
    }
    template <typename T>
    void Write(T x, char lst) {Write(x), Push(lst);}
} IO;
#define Read(x) IO.Read(x)
#define Write(x, y) IO.Write(x, y)
#define Put(x) IO.Push(x)

using namespace std;

const int MAXN = 5010, N = 5000;

int n; ll m;
bool e[MAXN][MAXN];

ll f[MAXN];
int a[MAXN][3];

inline int Calc()
{
    int cnt = 0;
    for (int i = 1; i <= n; i++)
        for (int j = i + 1; j <= n; j++)
            for (int k = j + 1; k <= n; k++)
                if ((e[i][j] && e[j][k] && e[k][i]) || (e[j][i] && e[k][j] && e[i][k]))
                    cnt++;
    return cnt;
}

inline void Link(int x, int y, int z, int ad)
{
    for (int i = 1; i <= x; i++)
        for (int j = x + 1; j <= x + y; j++)
            e[i + ad][j + ad] = 1;
    for (int i = x + 1; i <= x + y; i++)
        for (int j = x + y + 1; j <= x + y + z; j++)
            e[i + ad][j + ad] = 1;
    for (int i = x + y + 1; i <= x + y + z; i++)
        for (int j = 1; j <= x; j++)
            e[i + ad][j + ad] = 1;
}

inline void Full(int n, int ad)
{
    if (n <= 2) return;
    int x = a[n][0], y = a[n][1], z = a[n][2];
    Link(x, y, z, ad);
    Full(x, ad), Full(y, ad + x), Full(z, ad + x + y);
}

inline void Solve(int n, int m, int ad)
{
    if (m == 0) return;
    if (n <= 8 && !(n == 8 && m == 17))
    {
        for (int z = 0; z <= n; z++)
        for (int y = 0; y + z <= n; y++)
        for (int x = 0; x + y + z <= n; x++)
            if (x * y * z + f[x] + f[y] + f[z] == m) return Link(x, y, z, ad), Full(x, ad), Full(y, ad + x), Full(z, ad + x + y);
            else if (x * y * z == m) return Link(x, y, z, ad);
            else if (x * y * z + f[x] == m) return Link(x, y, z, ad), Full(x, ad);
            else if (z && x * y * (z - 1) + f[x] + f[y] + f[z] == m) return Link(x, y, z - 1, ad), Full(x, ad), Full(y, ad + x), Full(z, ad + x + y);
        cout << "Error " << n << ' ' << m << '\n';
        return;
    }
    ll x = a[n][0], y = a[n][1], z = a[n][2];
    if (x * y * (z - 1) < m)
    {
        if (m >= x * y * z) m -= x * y * z, Link(x, y, z, ad);
        else
        {
            m -= x * y * (z - 1), Link(x, y, z - 1, ad);
            ll _y = y;
            while (x * _y > m) _y--;
            for (int i = 1; i <= x; i++)
                for (int j = x + 1; j <= x + _y; j++)
                    e[i + ad][j + ad] = 1;
            for (int i = x + 1; i <= x + _y; i++)
                e[i + ad][x + y + z + ad] = 1;
            for (int i = 1; i <= x; i++)
                e[x + y + z + ad][i + ad] = 1;
            m -= x * _y;
        }
        if (m < f[x]) return Solve(x, m, ad);
        m -= f[x], Full(x, ad);
        if (m < f[y]) return Solve(y, m, ad + x);
        m -= f[y], Full(y, ad + x);
        if (m < f[z]) return Solve(z, m, ad + x + y);
        m -= f[z], Full(z, ad + x + y);
        return;
    }
    if (m <= x * y * (z - 1))
    {
        ll _z = z;
        while (x * y * _z > m) _z--;
        Link(x, y, _z, ad), m -= x * y * _z;
        if (!m) return;
        ll _y = y;
        while (x * _y > m) _y--;
        for (int i = 1; i <= x; i++)
            for (int j = x + 1; j <= x + _y; j++)
                e[i + ad][j + ad] = 1;
        for (int i = x + 1; i <= x + _y; i++)
            e[i + ad][x + y + z + ad] = 1;
        for (int i = 1; i <= x; i++)
            e[x + y + z + ad][i + ad] = 1;
        m -= x * _y;
        if (!m) return;
        for (int i = 1; i <= m; i++)
            e[i + ad][x + _y + 1 + ad] = e[x + y + z - 1 + ad][i + ad] = 1;
        e[x + _y + 1 + ad][x + y + z - 1 + ad] = 1;
    }
}

int main()
{
    // freopen("C.in", "r", stdin);
    // freopen("C.out", "w", stdout);
    #if DEBUG
    #else
    ios::sync_with_stdio(0), cin.tie(0);
    #endif

    for (int i = 3; i <= N; i++)
    {
        a[i][0] = a[i][1] = a[i][2] = i / 3;
        for (int j = 0; j < i % 3; j++) a[i][2 - j]++;
        for (int j = 0; j < 3; j++) f[i] += f[a[i][j]];
        f[i] += (ll)a[i][0] * a[i][1] * a[i][2];
    }

    int T;
    Read(T);
    while (T--)
    {
        Read(n), Read(m);
        for (int i = 1; i <= n; i++)
            for (int j = 1; j <= n; j++)
                e[i][j] = 0;
        if (f[n] < m) { cout << "No\n"; continue; }
        Solve(n, m, 0);
        cout << "Yes\n";
        for (int i = 2; i <= n; i++, cout << "\n")
            for (int j = 1; j < i; j++)
                cout << e[i][j];
        // int cnt = Calc();
        // if (cnt != m) cout << "WA " << n << ' ' << m << ' ' << cnt << "\n";
    }
    return 0;
}