Apply Operations to Maximize Score

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class Solution:
    MOD = 1000000007
    primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313]
    memo = [0] * 100001

    def mod_pow(self, x, y, m):
        if y == 0:
            return 1
        p = self.mod_pow(x, y // 2, m) % m
        p = (p * p) % m
        return (p * x) % m if y % 2 else p

    def prime_score(self, n):
        if self.memo[n]:
            return self.memo[n]
        score = 0
        val = n
        for i in range(65):
            if n < self.primes[i]:
                break
            if val % self.primes[i] == 0:
                score += 1
                while val % self.primes[i] == 0:
                    val //= self.primes[i]
        self.memo[n] = score + (val > 1)
        return self.memo[n]

    def maximumScore(self, nums: List[int], k: int) -> int:
        res = 1
        sz = len(nums)
        ids = list(range(sz))
        l = [0] * sz
        r = [0] * sz
        score_l = [-1] * 8
        score_r = [sz] * 8
        for i in range(sz):
            score = self.prime_score(nums[i])
            l[i] = max(score_l[score:])
            score_l[score] = i
        for i in range(sz - 1, -1, -1):
            score = self.prime_score(nums[i])
            r[i] = min(score_r[score + 1:])
            score_r[score] = i
        ids.sort(key=lambda x: -nums[x])
        while ids and k > 0:
            i = ids.pop(0)
            take = min(k, (i - l[i]) * (r[i] - i))
            res = (res * self.mod_pow(nums[i], take, self.MOD)) % self.MOD
            k -= take
        return res