1003.Maximum Sequence

Problem Description Steph is extremely obsessed with “sequence problems” that are usually seen on magazines: Given the sequence 11, 23, 30, 35, what is the next number? Steph always finds them too easy for such a genius like himself until one day Klay comes up with a problem and ask him about it. Given two integer sequences {ai} and {bi} with the same length n, you are to find the next n numbers of {ai}:an+1…a2n. Just like always, there are some restrictions on an+1…a2n: for each number ai, you must choose a number bk from {bi}, and it must satisfy ai≤max{aj−j|bk≤j<i}, and any bk can’t be chosen more than once. Apparently, there are a great many possibilities, so you are required to find max{∑2nn+1ai} modulo 109+7 . Now Steph finds it too hard to solve the problem, please help him. Input The input contains no more than 20 test cases. For each test case, the first line consists of one integer n. The next line consists of n integers representing {ai}. And the third line consists of n integers representing {bi}. 1≤n≤250000, n≤ai≤1500000, 1≤bi≤n. Output For each test case, print the answer on one line: max{∑2nn+1ai} modulo 109+7。 Sample Input 4 8 11 8 5 3 1 4 2 Sample Output 27 Hint For the first sample: 1. Choose 2 from {bi}, then a2…a4 are available for a5, and you can let a5=a2-2=9; 2. Choose 1 from {bi}, then a1…a5 are available for a6, and you can let a6=a2-2=9;

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