Dr. Evil is interested in math and functions, so he gave Mahmoud and Ehab array a of length n and array b of length m . He introduced a function f ( j ) which is defined for integers j , which satisfy 0 ≤ j ≤ m - n . Suppose, c i = a i - b i + j . Then f ( j ) = | c 1 - c 2 + c 3 - c 4 ... c n | . More formally, . Dr. Evil wants Mahmoud and Ehab to calculate the minimum value of this function over all valid j . They found it a bit easy, so Dr. Evil made their task harder. He will give them q update queries. During each update they should add an integer x i to all elements in a in range l i ; r i i.e. they should add x i to a l i , a l i + 1 , ... , a r i and then they should calculate the minimum value of f ( j ) for all valid j . Please help Mahmoud and Ehab. The first line contains three integers n , m and q ( 1 ≤ n ≤ m ≤ 10 5 , 1 ≤ q ≤ 10 5 ) — number of elements in a , number of elements in b and number of queries, respectively. The second line contains n integers a 1 , a 2 , ..., a n . ( - 10 9 ≤ a i ≤ 10 9 ) — elements of a . The third line contains m integers b 1 , b 2 , ..., b m . ( - 10 9 ≤ b i ≤ 10 9 ) — elements of b . Then q lines follow describing the queries. Each of them contains three integers l i r i x i ( 1 ≤ l i ≤ r i ≤ n , - 10 9 ≤ x ≤ 10 9 ) — range to be updated and added value. The first line should contain the minimum value of the function f before any update. Then output q lines, the i -th of them should contain the minimum value of the function f after performing the i -th update . For the first example before any updates it's optimal to choose j = 0 , f (0) = |(1 - 1) - (2 - 2) + (3 - 3) - (4 - 4) + (5 - 5)| = |0| = 0 . After the first update a becomes {11, 2, 3, 4, 5} and it's optimal to choose j = 1 , f (1) = |(11 - 2) - (2 - 3) + (3 - 4) - (4 - 5) + (5 - 6) = |9| = 9 . After the second update a becomes {2, 2, 3, 4, 5} and it's optimal to choose j = 1 , f (1) = |(2 - 2) - (2 - 3) + (3 - 4) - (4 - 5) + (5 - 6)| = |0| = 0 . A