# Time:  O(nlogn)
# Space: O(1)

# math, sort
class Solution(object):
    def maximumProduct(self, nums, k):
        """
        :type nums: List[int]
        :type k: int
        :rtype: int
        """
        MOD = 10**9+7
        nums.sort()
        total = sum(nums)
        for i in reversed(xrange(len(nums))):
            if nums[i]*(i+1)-total <= k:
                break
            total -= nums[i]
        q, r = divmod(k+total, i+1)
        return (pow(q, (i+1)-r, MOD)*pow(q+1, r, MOD)*
                reduce(lambda x, y: x*y%MOD, (nums[j] for j in xrange(i+1, len(nums))), 1)) % MOD


# Time:  O(n + k)
# Space: O(n)
import collections


# freq table
class Solution2(object):
    def maximumProduct(self, nums, k):
        """
        :type nums: List[int]
        :type k: int
        :rtype: int
        """
        MOD = 10**9+7
        cnt = collections.Counter(nums)
        min_num = min(cnt.iterkeys())
        while k:
            c = min(cnt[min_num], k)
            cnt[min_num] -= c
            cnt[min_num+1] += c 
            if not cnt[min_num]:
                del cnt[min_num]
                min_num += 1
            k -= c
        return reduce(lambda total, x: total*pow(x[0], x[1], MOD)%MOD, cnt.iteritems(), 1)


# Time:  O(n + klogn)
# Space: O(1)
import heapq


# heap
class Solution3(object):
    def maximumProduct(self, nums, k):
        """
        :type nums: List[int]
        :type k: int
        :rtype: int
        """
        MOD = 10**9+7
        min_heap = nums
        heapq.heapify(min_heap)
        while k:
            heapq.heappush(min_heap, heapq.heappop(min_heap)+1)
            k -= 1
        return reduce(lambda x, y: x*y%MOD, min_heap)