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

input = sys.stdin.buffer.readline

def find_pair(candidate,data,m):
    ans = (-1,-1)
    binary_bit = [False for i in range(1 << m)]
    for i in data:
        bit_tmp = 0
        for j in range(len(i)):
            if i[j] >= candidate: bit_tmp |= 1 << j
        binary_bit[bit_tmp] = True
    
    for i in range(1 << m):
        for j in range(1 << m):
            if i | j == (( 1 << m ) - 1) and binary_bit[i] and binary_bit[j]:
                ans = i , j
                break
    return ans

def backtracking(candidate,ans,data):
    idx_i = -1 ; idx_j = -1
    for i in range(len(data)):
        bit_tmp = 0
        for j in range(len(data[i])):
            if data[i][j] >= candidate: bit_tmp |= 1 << j
        if bit_tmp == ans[0]: idx_i = i
        if bit_tmp == ans[1]: idx_j = i

    print(str(idx_i + 1) + " " + str(idx_j + 1))

def main():
    n , m = [int(i) for i in input().split()]
    data = [[int(i) for i in input().split()] for i in range(n)]
    a = 0 ; b = 10**9 + 7
    ans = (-1,-1)
    candidate = -1
    while a <= b:
        mid = (a + b)//2
        bin_ans = find_pair(mid,data,m)
        if bin_ans[0] != -1 and bin_ans[1] != -1:
            ans = bin_ans
            candidate = mid
            a = mid + 1
        else:
            b = mid - 1
    backtracking(candidate,ans,data)

main()