Problem: Polycarpus has a computer with n processors. Also, his computer has n memory cells. We'll consider the processors numbered by integers from 1 to n and that the memory cells are consecutively numbered by integers from 1 to n.

Polycarpus needs to come up with a parallel program model. For each memory cell number i this program must record the value n - i to this cell. In other words, for each cell you've got to find the distance to cell n.

Let's denote the value that is written in the i-th cell as ai. Initially, ai = 1 (1 ≤ i < n) and an = 0. We will consider that only processor i can write values in the memory cell number i. All processors can read an information from some cell (several processors can read an information from some cell simultaneously).

The parallel program is executed in several steps. During each step we execute the parallel version of the increment operation. Executing the parallel version of the increment operation goes as follows:

  1. Each processor independently of the other ones chooses some memory cell. Let's say that processor i has chosen a cell with number ci (1 ≤ ci ≤ n). 
  2. All processors simultaneously execute operation ai = ai + aci. 



Help Polycarpus come up with the parallel program model that is executed in exactly k steps. Calculate the operations that need to be executed. Note that after k steps for all i's value ai must be equal n - i.

Input

The first line contains two space-separated integers n and k (1 ≤ n ≤ 104, 1 ≤ k ≤ 20).

It is guaranteed that at the given n and k the required sequence of operations exists.

Output

Print exactly n·k integers in k lines. In the first line print numbers c1, c2, ..., cn (1 ≤ ci ≤ n) for the first increment operation. In the second line print the numbers for the second increment operation. In the k-th line print the numbers for the k-th increment operation.

As a result of the printed operations for any i value ai must equal n - i.

Examples

Input

1 1


Output

1


Input

3 2


Output

2 3 3
3 3 3

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
template <class _T>
inline _T sqr(const _T &first) {
  return first * first;
}
template <class _T>
inline string tostr(const _T &a) {
  ostringstream os("");
  os << a;
  return os.str();
}
const long double PI = 3.1415926535897932384626433832795L;
const long double EPS = 1e-12;
char TEMPORARY_CHAR;
const int INF = 2e9;
inline void fft(vector<complex<long double> > &a, bool invert) {
  int n = (int)a.size();
  for (int i = 1, j = 0; i < n; ++i) {
    int bit = n >> 1;
    for (; j >= bit; bit >>= 1) j -= bit;
    j += bit;
    if (i < j) swap(a[i], a[j]);
  }
  for (int len = 2; len <= n; len <<= 1) {
    long double ang = 2 * PI / len * (invert ? -1 : 1);
    complex<long double> wlen(cos(ang), sin(ang));
    for (int i = 0; i < n; i += len) {
      complex<long double> w(1);
      for (int j = 0; j < len / 2; ++j) {
        complex<long double> u = a[i + j], v = a[i + j + len / 2] * w;
        a[i + j] = u + v;
        a[i + j + len / 2] = u - v;
        w *= wlen;
      }
    }
  }
  if (invert)
    for (int i = 0; i < n; ++i) a[i] /= n;
}
inline void input(int &a) {
  a = 0;
  while (((TEMPORARY_CHAR = getchar()) > '9' || TEMPORARY_CHAR < '0') &&
         (TEMPORARY_CHAR != '-')) {
  }
  char neg = 0;
  if (TEMPORARY_CHAR == '-') {
    neg = 1;
    TEMPORARY_CHAR = getchar();
  }
  while (TEMPORARY_CHAR <= '9' && TEMPORARY_CHAR >= '0') {
    a = (a << 3) + (a << 1) + TEMPORARY_CHAR - '0';
    TEMPORARY_CHAR = getchar();
  }
  if (neg) a = -a;
}
inline void out(int a) {
  if (!a) putchar('0');
  if (a < 0) {
    putchar('-');
    a = -a;
  }
  char s[10];
  int i;
  for (i = 0; a; ++i) {
    s[i] = '0' + a % 10;
    a /= 10;
  }
  for (int j = (i)-1; j >= 0; j--) putchar(s[j]);
}
inline int nxt() {
  int(ret);
  input((ret));
  ;
  return ret;
}
struct lnum {
  vector<int> a;
  int base;
  lnum(int num = 0, int base = 1000000000) : base(base) {
    if (!num) a.resize(1);
    while (num) {
      a.push_back(num % base);
      num /= base;
    }
  }
  inline int len() const { return a.size(); }
  lnum &operator=(const lnum &l) {
    if (this != &l) {
      a = l.a;
      base = l.base;
    }
    return *this;
  }
  inline friend lnum operator+(const lnum &l, const lnum &r) {
    lnum ret(0, l.base);
    int base = l.base;
    int ln = l.len(), rn = r.len();
    int n = max(ln, rn);
    ret.a.resize(n);
    int o = 0;
    for (int i = 0; i < n; ++i) {
      int s = o;
      if (i < ln) s += l.a[i];
      if (i < rn) s += r.a[i];
      o = s >= base;
      if (o) s -= base;
      ret.a[i] = s;
    }
    if (o) ret.a.push_back(1);
    return ret;
  }
  inline friend lnum operator-(const lnum &l, const lnum &r) {
    lnum ret(0, l.base);
    int base = l.base;
    int n = l.len();
    int rn = r.len();
    ret.a.resize(n);
    int o = 0;
    for (int i = 0; i < n; ++i) {
      int s = l.a[i] - o;
      if (i < rn) s -= r.a[i];
      o = s < 0;
      if (o) s += base;
      ret.a[i] = s;
    }
    if (ret.len() > 1 && !ret.a.back()) ret.a.pop_back();
    return ret;
  }
  inline friend lnum operator*(const lnum &l, const lnum &r) {
    lnum ret(0, l.base);
    int base = l.base;
    if (l.len() * r.len() > 1000000) {
      vector<complex<long double> > fa(l.a.begin(), l.a.end()),
          fb(r.a.begin(), r.a.end());
      int n = 1;
      while (n < max(l.len(), r.len())) n <<= 1;
      n <<= 1;
      fa.resize(n), fb.resize(n);
      fft(fa, false), fft(fb, false);
      for (int i = 0; i < n; ++i) fa[i] *= fb[i];
      fft(fa, true);
      ret.a.resize(n);
      for (int i = 0; i < n; ++i) ret.a[i] = int(fa[i].real() + 0.5);
      int carry = 0;
      for (int i = 0; i < n; ++i) {
        ret.a[i] += carry;
        carry = ret.a[i] / base;
        ret.a[i] %= base;
      }
    } else {
      ret.a.resize(l.len() + r.len());
      for (int i = 0; i < l.len(); ++i)
        for (int j = 0, carry = 0; j < r.len() || carry; ++j) {
          long long cur = ret.a[i + j] +
                          (long long)l.a[i] * (j < r.len() ? r.a[j] : 0) +
                          carry;
          ret.a[i + j] = cur % base;
          carry = cur / base;
        }
    }
    while (ret.len() > 1 && !ret.a.back()) ret.a.pop_back();
    return ret;
  }
  inline friend lnum operator/(const lnum &l, const int &r) {
    lnum ret(0, l.base);
    ret.a.resize(l.len());
    int carry = 0;
    for (int i = l.len() - 1; i >= 0; --i) {
      long long cur = l.a[i] + (long long)carry * l.base;
      ret.a[i] = cur / r;
      carry = cur % r;
    }
    while (ret.len() > 1 && ret.a.back() == 0) ret.a.pop_back();
    return ret;
  }
  inline friend bool operator<(const lnum &l, const lnum &r) {
    if (l.len() < r.len()) return true;
    if (l.len() > r.len()) return false;
    int n = l.len();
    for (int i = n - 1; i >= 0; --i) {
      if (l.a[i] < r.a[i]) return true;
      if (l.a[i] > r.a[i]) return false;
    }
    return false;
  }
  inline friend bool operator>(const lnum &l, const lnum &r) { return r < l; }
  inline friend bool operator==(const lnum &l, const lnum &r) {
    if (l.len() != r.len()) return false;
    int n = l.len();
    for (int i = n - 1; i; --i) {
      if (l.a[i] != r.a[i]) return false;
    }
    return true;
  }
  inline friend bool operator!=(const lnum &l, const lnum &r) {
    return !(l == r);
  }
  inline void print() {
    if (base == 1000000000) {
      printf("%d", a.back());
      for (int i = a.size() - 2; i >= 0; --i) printf("%09d", a[i]);
    } else {
      for (int i = a.size() - 1; i >= 0; --i) printf("%d", a[i]);
    }
  }
};
int main() {
  int(n);
  input((n));
  ;
  int(k);
  input((k));
  ;
  for (int i = 0; i < (int)(k); i++) {
    int solve = 1 << i;
    for (int j = 0; j < (int)(n - 2 * solve - 1); j++) {
      printf("%d ", n - solve);
    }
    for (int j = (max(1, n - 2 * solve)); j <= (int)(max(1, n - solve) - 1);
         j++) {
      int cur = j - (n - 2 * solve);
      printf("%d ", n - solve + cur);
    }
    for (int j = (max(1, n - solve)); j <= (int)(n); j++) {
      printf("%d ", n);
    }
    printf("\n");
  }
  return 0;
}