Score : 1000 points

Problem Statement

There is a simple undirected graph with N vertices and M edges. The vertices are numbered 1 through N, and the edges are numbered 1 through M. Edge i connects Vertex U_i and V_i. Also, Vertex i has two predetermined integers A_i and B_i. You will play the following game on this graph.

First, choose one vertex and stand on it, with W yen (the currency of Japan) in your pocket. Here, A_s \leq W must hold, where s is the vertex you choose. Then, perform the following two kinds of operations any number of times in any order:

  • Choose one vertex v that is directly connected by an edge to the vertex you are standing on, and move to vertex v. Here, you need to have at least A_v yen in your pocket when you perform this move.
  • Donate B_v yen to the vertex v you are standing on. Here, the amount of money in your pocket must not become less than 0 yen.

You win the game when you donate once to every vertex. Find the smallest initial amount of money W that enables you to win the game.

Constraints

  • 1 \leq N \leq 10^5
  • N-1 \leq M \leq 10^5
  • 1 \leq A_i,B_i \leq 10^9
  • 1 \leq U_i < V_i \leq N
  • The given graph is connected and simple (there is at most one edge between any pair of vertices).

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
A_2 B_2
:
A_N B_N
U_1 V_1
U_2 V_2
:
U_M V_M

Output

Print the smallest initial amount of money W that enables you to win the game.

Sample Input 1

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

Sample Output 1

6

If you have 6 yen initially, you can win the game as follows:

  • Stand on Vertex 4. This is possible since you have not less than 6 yen.
  • Donate 2 yen to Vertex 4. Now you have 4 yen.
  • Move to Vertex 3. This is possible since you have not less than 4 yen.
  • Donate 1 yen to Vertex 3. Now you have 3 yen.
  • Move to Vertex 2. This is possible since you have not less than 1 yen.
  • Move to Vertex 1. This is possible since you have not less than 3 yen.
  • Donate 1 yen to Vertex 1. Now you have 2 yen.
  • Move to Vertex 2. This is possible since you have not less than 1 yen.
  • Donate 2 yen to Vertex 2. Now you have 0 yen.

If you have less than 6 yen initially, you cannot win the game. Thus, the answer is 6.

Sample Input 2

5 8
6 4
15 13
15 19
15 1
20 7
1 3
1 4
1 5
2 3
2 4
2 5
3 5
4 5

Sample Output 2

44

Sample Input 3

9 10
131 2
98 79
242 32
231 38
382 82
224 22
140 88
209 70
164 64
6 8
1 6
1 4
1 3
4 7
4 9
3 7
3 9
5 9
2 5

Sample Output 3

582