[EC Final 2022] Chase Game

题目描述

Prof. Shou is being chased by Prof. Pang on an undirected unweighted simple graph. Initially, Prof. Shou is at vertex $1$. His destination is vertex $n$. Prof. Pang is at vertex $k$. In each second, Prof. Shou may choose an adjacent vertex and walk to that vertex. Then Prof. Shou is attacked by Prof. Pang. The damage of this attack is equal to $d-dis$ where $d$ is Prof. Pang's attack range and $dis$ is the distance (number of edges in the shortest path) between Prof. Shou and Prof. Pang on the graph. However, when $dis$ is greater than or equal to $d$, Prof. Pang cannot deal any positive damage. In this case, instead of attacking with non-positive damage, he will teleport to the vertex where Prof. Shou is and then deal $d$ damage. (When $dis$ is less than $d$, Prof. Pang will stay at his current vertex.) Please find the minimum sum of damage Prof. Shou will take to reach vertex $n$ from vertex $1$. Prof. Shou will take the last attack at vertex $n$.

输入输出格式

输入格式


The first line contains $4$ integers $n, m, k, d$ ($2\le n\le 10^5, n-1\le m\le 2\times 10^5, 1\le k\le n, 1\le d\le 2\times 10^5$). Each of the next $m$ lines contains two integers $a, b$ ($1\le a, b\le n, a \ne b$) representing an edge of the graph. The edges are distinct. ($a\ b$ and $b\ a$ represents the same edge. Thus, only one of these two lines may appear in the input.) It is guaranteed that the graph is connected.

输出格式


Output one integer representing the answer in one line.

输入输出样例

输入样例 #1

5 5 3 1
1 2
2 4
4 5
1 3
3 5

输出样例 #1

2

输入样例 #2

13 17 12 3
1 2
2 3
3 4
4 13
5 13
7 8
7 9
7 10
7 11
7 6
12 7
1 8
8 9
9 10
10 11
11 6
6 13

输出样例 #2

7