As the ruler of a kingdom, you have an army of wizards at your command.
\n\nYou are given a 0-indexed integer array strength, where strength[i] denotes the strength of the ith wizard. For a contiguous group of wizards (i.e. the wizards' strengths form a subarray of strength), the total strength is defined as the product of the following two values:
Return the sum of the total strengths of all contiguous groups of wizards. Since the answer may be very large, return it modulo 109 + 7.
A subarray is a contiguous non-empty sequence of elements within an array.
\n\n\n
Example 1:
\n\n\nInput: strength = [1,3,1,2]\nOutput: 44\nExplanation: The following are all the contiguous groups of wizards:\n- [1] from [1,3,1,2] has a total strength of min([1]) * sum([1]) = 1 * 1 = 1\n- [3] from [1,3,1,2] has a total strength of min([3]) * sum([3]) = 3 * 3 = 9\n- [1] from [1,3,1,2] has a total strength of min([1]) * sum([1]) = 1 * 1 = 1\n- [2] from [1,3,1,2] has a total strength of min([2]) * sum([2]) = 2 * 2 = 4\n- [1,3] from [1,3,1,2] has a total strength of min([1,3]) * sum([1,3]) = 1 * 4 = 4\n- [3,1] from [1,3,1,2] has a total strength of min([3,1]) * sum([3,1]) = 1 * 4 = 4\n- [1,2] from [1,3,1,2] has a total strength of min([1,2]) * sum([1,2]) = 1 * 3 = 3\n- [1,3,1] from [1,3,1,2] has a total strength of min([1,3,1]) * sum([1,3,1]) = 1 * 5 = 5\n- [3,1,2] from [1,3,1,2] has a total strength of min([3,1,2]) * sum([3,1,2]) = 1 * 6 = 6\n- [1,3,1,2] from [1,3,1,2] has a total strength of min([1,3,1,2]) * sum([1,3,1,2]) = 1 * 7 = 7\nThe sum of all the total strengths is 1 + 9 + 1 + 4 + 4 + 4 + 3 + 5 + 6 + 7 = 44.\n\n\n
Example 2:
\n\n\nInput: strength = [5,4,6]\nOutput: 213\nExplanation: The following are all the contiguous groups of wizards: \n- [5] from [5,4,6] has a total strength of min([5]) * sum([5]) = 5 * 5 = 25\n- [4] from [5,4,6] has a total strength of min([4]) * sum([4]) = 4 * 4 = 16\n- [6] from [5,4,6] has a total strength of min([6]) * sum([6]) = 6 * 6 = 36\n- [5,4] from [5,4,6] has a total strength of min([5,4]) * sum([5,4]) = 4 * 9 = 36\n- [4,6] from [5,4,6] has a total strength of min([4,6]) * sum([4,6]) = 4 * 10 = 40\n- [5,4,6] from [5,4,6] has a total strength of min([5,4,6]) * sum([5,4,6]) = 4 * 15 = 60\nThe sum of all the total strengths is 25 + 16 + 36 + 36 + 40 + 60 = 213.\n\n\n
\n
Constraints:
\n\n1 <= strength.length <= 1051 <= strength[i] <= 109作为国王的统治者，你有一支巫师军队听你指挥。
\n\n给你一个下标从 0 开始的整数数组 strength ，其中 strength[i] 表示第 i 位巫师的力量值。对于连续的一组巫师（也就是这些巫师的力量值是 strength 的 子数组），总力量 定义为以下两个值的 乘积 ：
请你返回 所有 巫师组的 总 力量之和。由于答案可能很大，请将答案对 109 + 7 取余 后返回。
子数组 是一个数组里 非空 连续子序列。
\n\n\n\n
示例 1：
\n\n输入：strength = [1,3,1,2]\n输出：44\n解释：以下是所有连续巫师组：\n- [1,3,1,2] 中 [1] ，总力量值为 min([1]) * sum([1]) = 1 * 1 = 1\n- [1,3,1,2] 中 [3] ，总力量值为 min([3]) * sum([3]) = 3 * 3 = 9\n- [1,3,1,2] 中 [1] ，总力量值为 min([1]) * sum([1]) = 1 * 1 = 1\n- [1,3,1,2] 中 [2] ，总力量值为 min([2]) * sum([2]) = 2 * 2 = 4\n- [1,3,1,2] 中 [1,3] ，总力量值为 min([1,3]) * sum([1,3]) = 1 * 4 = 4\n- [1,3,1,2] 中 [3,1] ，总力量值为 min([3,1]) * sum([3,1]) = 1 * 4 = 4\n- [1,3,1,2] 中 [1,2] ，总力量值为 min([1,2]) * sum([1,2]) = 1 * 3 = 3\n- [1,3,1,2] 中 [1,3,1] ，总力量值为 min([1,3,1]) * sum([1,3,1]) = 1 * 5 = 5\n- [1,3,1,2] 中 [3,1,2] ，总力量值为 min([3,1,2]) * sum([3,1,2]) = 1 * 6 = 6\n- [1,3,1,2] 中 [1,3,1,2] ，总力量值为 min([1,3,1,2]) * sum([1,3,1,2]) = 1 * 7 = 7\n所有力量值之和为 1 + 9 + 1 + 4 + 4 + 4 + 3 + 5 + 6 + 7 = 44 。\n\n\n
示例 2：
\n\n输入：strength = [5,4,6]\n输出：213\n解释：以下是所有连续巫师组：\n- [5,4,6] 中 [5] ，总力量值为 min([5]) * sum([5]) = 5 * 5 = 25\n- [5,4,6] 中 [4] ，总力量值为 min([4]) * sum([4]) = 4 * 4 = 16\n- [5,4,6] 中 [6] ，总力量值为 min([6]) * sum([6]) = 6 * 6 = 36\n- [5,4,6] 中 [5,4] ，总力量值为 min([5,4]) * sum([5,4]) = 4 * 9 = 36\n- [5,4,6] 中 [4,6] ，总力量值为 min([4,6]) * sum([4,6]) = 4 * 10 = 40\n- [5,4,6] 中 [5,4,6] ，总力量值为 min([5,4,6]) * sum([5,4,6]) = 4 * 15 = 60\n所有力量值之和为 25 + 16 + 36 + 36 + 40 + 60 = 213 。\n\n\n
\n\n
提示：
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