Maximum Sum Obtained of Any Permutation — Python

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

import itertools


class Solution(object):
    def maxSumRangeQuery(self, nums, requests):
        """
        :type nums: List[int]
        :type requests: List[List[int]]
        :rtype: int
        """
        def addmod(a, b, mod):  # avoid overflow in other languages
            a %= mod
            b %= mod
            if mod-a <= b:
                b -= mod
            return a+b
        
        def mulmod(a, b, mod):  # avoid overflow in other languages
            a %= mod
            b %= mod
            if a < b:
                a, b = b, a
            result = 0
            while b > 0:
                if b%2 == 1:
                    result = addmod(result, a, mod)
                a = addmod(a, a, mod)
                b //= 2
            return result

        MOD = 10**9+7

        count = [0]*len(nums)
        for start, end in requests:
            count[start] += 1
            if end+1 < len(count):
                count[end+1] -= 1
        for i in xrange(1, len(count)):
            count[i] += count[i-1]
        nums.sort()
        count.sort()
        result = 0
        for i, (num, c) in enumerate(itertools.izip(nums, count)):
            # result = addmod(result, mulmod(num, c, MOD), MOD)
            result = (result+num*c)%MOD
        return result