human
Can you provide a Python code to find out how many boxes and of which type should Dima buy to transport maximum number of hamsters given the following:
Dima has a hamsters farm. Soon N hamsters will grow up on it and Dima will sell them in a city nearby.

Hamsters should be transported in boxes. If some box is not completely full, the hamsters in it are bored, that's why each box should be completely full with hamsters.

Dima can buy boxes at a factory. The factory produces boxes of K kinds, boxes of the i-th kind can contain in themselves ai hamsters. Dima can buy any amount of boxes, but he should buy boxes of only one kind to get a wholesale discount.

Of course, Dima would buy boxes in such a way that each box can be completely filled with hamsters and transported to the city. If there is no place for some hamsters, Dima will leave them on the farm.

Find out how many boxes and of which type should Dima buy to transport maximum number of hamsters.

Input

The first line contains two integers N and K (0 ≤ N ≤ 1018, 1 ≤ K ≤ 105) — the number of hamsters that will grow up on Dima's farm and the number of types of boxes that the factory produces.

The second line contains K integers a1, a2, ..., aK (1 ≤ ai ≤ 1018 for all i) — the capacities of boxes.

Output

Output two integers: the type of boxes that Dima should buy and the number of boxes of that type Dima should buy. Types of boxes are numbered from 1 to K in the order they are given in input.

If there are many correct answers, output any of them.

Examples

Input

19 3
5 4 10

Output

2 4

Input

28 3
5 6 30

Output

1 5
The above is tricky. Write me a correct solution in PYTHON3.
assistant
#Here is Python code to find out how many boxes and of which type should Dima buy to transport maximum number of hamsters.

from sys import stdin as si
from collections import Counter as c

class Solution:

    def bazinga(self, n,m):
        if n==0:    return '1 0'
        l,b = n, 0
        ans = [1,b]
        for i in range(len(m)):
            bb = n//m[i]
            ll = n%m[i]
            if ll < l:
                ans[0] = i+1
                ans[1] = bb
                l,b =ll, bb
            elif ll==l:
                if ans[1] < bb:
                    ans[0] = i+1
                    ans[1] = bb
                    l, b = ll, bb

        return ' '.join(map(str,ans))

if __name__ == '__main__':
    #for i in range(int(si.readline().strip())):
    n, k = map(int, si.readline().strip().split())
    m = list(map(int, si.readline().strip().split()))
    S = Solution()
    print(S.bazinga(n, m))

'''
http://codeforces.com/contest/939/problem/B
'''