Missile Silos

题意翻译

给定一张连通的无向图，求其中有多少秘密基地。所谓一个秘密基地，就是距离s号点的最短距离恰好等于k的位置，这个位置可以在一个结点上，也可以在一条边的中间。

题目描述

A country called Berland consists of $ n $ cities, numbered with integer numbers from $ 1 $ to $ n $ . Some of them are connected by bidirectional roads. Each road has some length. There is a path from each city to any other one by these roads. According to some Super Duper Documents, Berland is protected by the Super Duper Missiles. The exact position of the Super Duper Secret Missile Silos is kept secret but Bob managed to get hold of the information. That information says that all silos are located exactly at a distance $ l $ from the capital. The capital is located in the city with number $ s $ . The documents give the formal definition: the Super Duper Secret Missile Silo is located at some place (which is either city or a point on a road) if and only if the shortest distance from this place to the capital along the roads of the country equals exactly $ l $ . Bob wants to know how many missile silos are located in Berland to sell the information then to enemy spies. Help Bob.

输入输出格式

输入格式

The first line contains three integers $ n $ , $ m $ and $ s $ ( $ 2<=n<=10^{5} $ , , $ 1<=s<=n $ ) — the number of cities, the number of roads in the country and the number of the capital, correspondingly. Capital is the city no. $ s $ . Then $ m $ lines contain the descriptions of roads. Each of them is described by three integers $ v_{i} $ , $ u_{i} $ , $ w_{i} $ ( $ 1<=v_{i},u_{i}<=n $ , $ v_{i}≠u_{i} $ , $ 1<=w_{i}<=1000 $ ), where $ v_{i} $ , $ u_{i} $ are numbers of the cities connected by this road and $ w_{i} $ is its length. The last input line contains integer $ l $ ( $ 0<=l<=10^{9} $ ) — the distance from the capital to the missile silos. It is guaranteed that: - between any two cities no more than one road exists; - each road connects two different cities; - from each city there is at least one way to any other city by the roads.

输出格式

Print the single number — the number of Super Duper Secret Missile Silos that are located in Berland.

输入输出样例

输入样例 #1

4 6 1
1 2 1
1 3 3
2 3 1
2 4 1
3 4 1
1 4 2
2

输出样例 #1

3

输入样例 #2

5 6 3
3 1 1
3 2 1
3 4 1
3 5 1
1 2 6
4 5 8
4

输出样例 #2

3

说明

In the first sample the silos are located in cities $ 3 $ and $ 4 $ and on road $ (1,3) $ at a distance $ 2 $ from city $ 1 $ (correspondingly, at a distance $ 1 $ from city $ 3 $ ). In the second sample one missile silo is located right in the middle of the road $ (1,2) $ . Two more silos are on the road $ (4,5) $ at a distance $ 3 $ from city $ 4 $ in the direction to city $ 5 $ and at a distance $ 3 $ from city $ 5 $ to city $ 4 $ .