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문제

Given two sets P and Q of finitely many points in the plane, a closest pair of P and Q is a pair (p, q) of points p ∈ P and q ∈ Q such that the distance between p and q is the minimum among all pairs (p′, q′) with p′ ∈ P and q′ ∈ Q.

Specifically, in this problem, by the distance between two points a and b in the plane, we mean:

d(a, b) = |xa - xb| + |ya - yb|

where xa and ya denote the x- and y-coordinates of point a, and xb and yb denote the x- and y-coordinates of point b. Then, a pair (p, q) with p ∈ P and q ∈ Q is a closest pair of P and Q if and only if the following holds:

d(p, q) = min{ d(p′, q′) | p′ ∈ P and q′ ∈ Q}

Given two sets P and Q, write a program that computes the distance between a closest pair of P and Q and the number of distinct closest pairs of P and Q.

Note that you can assume the following on the input points in P and Q:

  1. All the points in P lie on the horizontal line y = c1 while all the points in Q lie on the horizontal line y = c2 for some integers c1 and c2.
  2. No two input points in P have the same coordinates; no two input points in Q have the same coordinates.

입력

Your program is to read from standard input. The input consists of four lines. The first line contains two integers, n (1 ≤ n ≤ 500,000) and m (1 ≤ m ≤ 500,000), where n is the number of points in set P and m is the number of points in set Q. In the second line, two integers c1 and c2 (-108 ≤ c1, c2 ≤ 108) are given in order, separated by a single space. In the third line, n distinct integers between -108 and 108, inclusively, are given, separated by a single space, that are the x-coordinates of the points in set P, while their y- coordinates are all the same as c1. In the fourth line, m distinct integers between -108 and 108, inclusively, are given, separated by a single space, that are the x-coordinates of the points in set Q, while their y- coordinates are all the same as c2.

출력

Your program is to write to standard output. Print exactly one line for the input. The line should contain two integers, separated by a single space, that represent the distance between a closest pair of P and Q and the number of closest pairs of P and Q in this order.

예제 입력 1

3 4
1 -3
3 0 6
-2 5 4 2

예제 출력 1

5 3

예제 입력 2

5 5
1 2
-4 -10 -2 0 -1
3 18 0 1 5

예제 출력 2

1 1

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