Problem: You are given n arrays a_1, a_2, ..., a_n; each array consists of exactly m integers. We denote the y-th element of the x-th array as a_{x, y}.

You have to choose two arrays a_i and a_j (1 ≤ i, j ≤ n, it is possible that i = j). After that, you will obtain a new array b consisting of m integers, such that for every k ∈ [1, m] b_k = max(a_{i, k}, a_{j, k}).

Your goal is to choose i and j so that the value of min _{k = 1}^{m} b_k is maximum possible.

Input

The first line contains two integers n and m (1 ≤ n ≤ 3 ⋅ 10^5, 1 ≤ m ≤ 8) — the number of arrays and the number of elements in each array, respectively.

Then n lines follow, the x-th line contains the array a_x represented by m integers a_{x, 1}, a_{x, 2}, ..., a_{x, m} (0 ≤ a_{x, y} ≤ 10^9).

Output

Print two integers i and j (1 ≤ i, j ≤ n, it is possible that i = j) — the indices of the two arrays you have to choose so that the value of min _{k = 1}^{m} b_k is maximum possible. If there are multiple answers, print any of them.

Example

Input


6 5
5 0 3 1 2
1 8 9 1 3
1 2 3 4 5
9 1 0 3 7
2 3 0 6 3
6 4 1 7 0


Output


1 5

Solution (in PYTHON3):

Solution:
import sys
from array import array  # noqa: F401
from typing import Dict, List, Tuple, TypeVar, Generic, Sequence, Union  # noqa: F401


def input():
    return sys.stdin.buffer.readline().decode('utf-8')


def main():
    n, m = map(int, input().split())
    mat = [array('i', map(int, input().split())) for _ in range(n)]
    bit = array('h', [1 << i for i in range(m)])
    max_bit = 1 << m
    fullbit = max_bit - 1

    def solve(x: int) -> Tuple[int, int]:
        dp = array('i', [-1]) * max_bit
        for i in range(n):
            dp[sum(bit[j] for j in range(m) if mat[i][j] >= x)] = i

        for i in range(max_bit):
            if dp[i] == -1:
                continue
            for j in range(i, max_bit):
                if dp[j] != -1 and i | j == fullbit:
                    return dp[i], dp[j]

        return -1, -1

    ok, ng = 0, 10**9 + 1
    ans_i, ans_j = 1, 1

    while abs(ok - ng) > 1:
        mid = (ok + ng) >> 1
        x, y = solve(mid)
        if x == -1:
            ng = mid
        else:
            ok = mid
            ans_i, ans_j = x + 1, y + 1

    print(ans_i, ans_j)


if __name__ == '__main__':
    main()