Finding a Hidden Benchmark Value

You are given array A with N number A= [a0, a1 .. aN-1] and array B with M numbers, B= [b0, b1 ... bM-1]. (1≤ N, M≤ 10 ^5,1 ≤ ais ≤ 10⁸, 1≤ bj ≤ 10⁸) SA and SB represent the respective scores of A and B, and each score is defined as the total score of the elements in each array. When calculating SA and SB this way, calculate D which makes the biggest difference between the two. (Caution: It is Not the absolute value) If there is more than one D that maximizes the difference between SA and SB, Calculate the smallest one.

Constraints

• 1 ≤ N, M ≤ 10⁵
• 1 ≤ a_i ≤ 10⁸
• 1 ≤ b_j ≤ 10⁸

Example 1

Input:

A = [6, 10, 9, 7, 8]
B = [4, 1, 5, 3, 2]

Output:

5

Explanation: When D is 5, the score of A and B are 10 and 5, respectively. Then, the value of SA-SB is 5 which is also maximum.

Example 2

Input:

A = [3, 2, 1]
B = [5, 6]

Output:

0

Explanation: When D is 0, the scores of A and B are 6 and 4 respectively. Then, the value of SA-SB is 2 which is also maximum.

Example 3

Input:

A = [10, 6, 3]
B = [3, 3, 10, 3, 2, 11]

Output:

3

Explanation: When D is 3, the scores of A and B are 5 and 8 respectively. Then, the value of SA-SB is -3 which is also maximum. Although the maximum value of SA-SB is -3 when D is 11 or 12 as the score of A and B are 3 and 6, respectively, the answer is 3 because 3 is smaller than 11.

Example 4

Input:

A = [1, 2]
B = [5, 6, 7, 8]

Output:

8

Explanation: When D is 8, the scores of A and B are 2 and 4 respectively. Then, the value of SA-SB is -2 which is also maximum. Remember that the difference between SA and SB is not an absolute value.