We have a grid with (2^N - 1) rows and (2^M-1) columns. You are asked to write 0 or 1 in each of these squares. Let a_{i,j} be the number written in the square at the i-th row from the top and the j-th column from the left.

For a quadruple of integers (i_1, i_2, j_1, j_2) such that 1\leq i_1 \leq i_2\leq 2^N-1, 1\leq j_1 \leq j_2\leq 2^M-1, let S(i_1, i_2, j_1, j_2) = \displaystyle \sum_{r=i_1}^{i_2}\sum_{c=j_1}^{j_2}a_{r,c}. Then, let the oddness of the grid be the number of quadruples (i_1, i_2, j_1, j_2) such that S(i_1, i_2, j_1, j_2) is odd.

Find a way to fill in the grid that maximizes its oddness.

Constraints

* N and M are integers between 1 and 10 (inclusive).

Input

Input is given from Standard Input in the following format:


N M


Output

Print numbers to write in the grid so that its oddness is maximized, in the following format:


a_{1,1}a_{1,2}\cdots a_{1,2^M-1}
a_{2,1}a_{2,2}\cdots a_{2,2^M-1}
\vdots
a_{2^N-1,1}a_{2^N-1,2}\cdots a_{2^N-1,2^M-1}


If there are multiple solutions, you can print any of them.

Example

Input

1 2


Output

111
#include <bits/stdc++.h>
// #pragma GCC optimize("Ofast")
// #pragma GCC target("avx,avx2,fma")
// #pragma GCC optimize("unroll-loops")
using namespace std;
typedef long long ll;

namespace Math {
    ll modpow(ll b, ll p, ll m) {
        ll r = 1;
        for (; p; p >>= 1, b = b * b % m)
            if (p & 1)
                r = r * b % m;
        return r;
    }

    ll modinv(ll b, ll m) { return modpow(b, m - 2, m); }

    // Least significant bit.
    ll lsb(ll x) { return x & (-x); }

    template <class T> const T inf() { return 0; }
    template <> const ll inf<ll>() { return 0x3f3f3f3f3f3f3f3fll; }
    template <> const int inf<int>() { return 0x3f3f3f3f; }

    template <class T> T gcd(T a, T b) { return abs(__gcd(a, b)); }
    template <class T> T clamp(T n, T l, T r) { return n < l ? l : n > r ? r : n; }
    template <class T> T lcm(T a, T b) { return abs(a / gcd(a, b) * b); }
    template <class T> T sgn(T n) { return n == 0 ? 0 : n > 0 ? 1 : -1; }

    // Generic modular integer.
    template<int MOD, typename IntType = int>
    struct GModint {
        IntType val;

        GModint() : val(0) {}

        GModint(int v, bool safe = false) { val = safe ? v : ((v % MOD) + MOD) % MOD; }

        GModint(ll v, bool safe = false) { val = safe ? v : ((v % MOD) + MOD) % MOD; }

        explicit operator bool() const { return val != 0; }

        const bool operator==(const GModint &g) const { return val == g.val; }

        const bool operator!=(const GModint &g) const { return val != g.val; }

        const GModint operator+=(const GModint &g) { return *this = *this + g; }

        const GModint operator-=(const GModint &g) { return *this = *this - g; }

        const GModint operator*=(const GModint &g) { return *this = *this * g; }

        const GModint operator/=(const GModint &g) { return *this = *this / g; }

        const GModint operator^=(const GModint &g) { return *this = *this ^ g; }

        const GModint operator-() const { return GModint(val == 0 ? 0 : MOD - val, true); }

        const GModint operator+(const GModint &g) const {
            ll newval = val + g.val;
            if (newval >= MOD)
                newval -= MOD;
            return GModint(newval, true);
        }

        const GModint operator-(const GModint &g) const { return *this + (-g); }

        const GModint operator*(const GModint &g) const { return GModint(1ll * val * g.val); }

        const GModint operator/(const GModint &g) const { return *this * g.inv(); }

        template<class T>
        const GModint operator^(const T t) const { return GModint(modpow(val, t, MOD)); }

        const GModint inv() const { return GModint(modinv(val, MOD)); }
    };

    using Modint = GModint<1000000007>;
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);

    int n, m; cin >> n >> m;
    for (int i = 1; i <= ((1 << n) - 1); i++) {
        for (int j = 1; j <= ((1 << m) - 1); j++) {
            int li = i & -i;
            int lj = j & -j;
            cout << (li == lj ? 1 : 0) << "";
        }
        cout << endl;
    }
}
