B'This is the hard version of the problem. The difference between the two versions is that you have to minimize the number of operations in this version. You can make hacks only if both versions of the problem are solved. You have two permutations ^{ dagger} p_{1}, p_{2}, ldots, p_{n} (of integers 1 to n ) and q_{1}, q_{2}, ldots, q_{m} (of integers 1 to m ). Initially p_{i}=a_{i} for i=1, 2, ldots, n , and q_{j} = b_{j} for j = 1, 2, ldots, m . You can apply the following operation on the permutations several (possibly, zero) times. In one operation, p and q will change according to the following three steps: Your goal is to simultaneously make p_{i}=i for i=1, 2, ldots, n , and q_{j} = j for j = 1, 2, ldots, m . Find any way to achieve the goal using the minimum number of operations possible, or say that none exists. Please note that you have to minimize the number of operations. ^{ dagger} A permutation of length k is an array consisting of k distinct integers from 1 to k in arbitrary order. For example, [2,3,1,5,4] is a permutation, but [1,2,2] is not a permutation ( 2 appears twice in the array), and [1,3,4] is also not a permutation ( k=3 but there is 4 in the array). The first line contains two integers n and m ( 1 <= n, m <= 2500 ). The second line contains n integers a_1, a_2, ldots, a_n ( 1 <= a_i <= n ). The third line contains m integers b_1, b_2, ldots, b_m ( 1 <= b_i <= m ). It is guaranteed that a and b are permutations. If there is no solution, print a single integer -1 . Otherwise, print an integer k -- the number of operations to perform, followed by k lines, each containing two integers i and j ( 1 <= i <= n , 1 <= j <= m ) -- the integers chosen for the operation. '...