Problem Statement

In the Republic of AtCoder, there are N cities numbered 1 through N and M railroads numbered 1 through M.
Railroad i connects City A_i and City B_i bidirectionally. At time 0, K_i, and all subsequent multiples of K_i, a train departs from each of these cities and head to the other city. The time each of these trains takes to reach the destination is T_i.
You are now at City X. Find the earliest time you can reach City Y when you start the journey by taking a train that departs City X not earlier than time 0. If City Y is unreachable, report that fact.
The time it takes to transfer is ignorable. That is, at every city, you can transfer to a train that departs at the exact time your train arrives at that city.

Input

Input is given from Standard Input in the following format:
N M X Y
A_1 B_1 T_1 K_1
$\vdots$
A_M B_M T_M K_M

Output

Print the earliest possible time you can reach City Y. If City Y is unreachable, print -1 instead.

Constraints

• $2 \leq N \leq 10^5$
• $0 \leq M \leq 10^5$
• $1 \leq X,Y \leq N$
• $X \neq Y$
• $1 \leq A_i,B_i \leq N$
• $A_i \neq B_i$
• $1 \leq T_i \leq 10^9$
• $1 \leq K_i \leq 10^9$
• All values in input are integers.

Sample Input 1

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

Sample Output 1

7

First, you take Railroad 1 at time 0 and go from City 1 to City 2. You arrive at City 2 at time 2.
Then, you take Railroad 2 at time 4 and go from City 2 to City 3. You arrive at City 3 at time 7.
There is no way to reach City 3 earlier.

Sample Input 2

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

Sample Output 2

5

First, you take Railroad 2 at time 0 and go from City 3 to City 2. You arrive at City 2 at time 3.
Then, you take Railroad 1 at time 3 and go from City 2 to City 1. You arrive at City 1 at time 5.

Sample Input 3

3 0 3 1

Sample Output 3

-1

Sample Input 4

9 14 6 7
3 1 4 1
5 9 2 6
5 3 5 8
9 7 9 3
2 3 8 4
6 2 6 4
3 8 3 2
7 9 5 2
8 4 1 9
7 1 6 9
3 9 9 3
7 5 1 5
8 2 9 7
4 9 4 4

Sample Output 4

26

见题面 Input 部分

见题面 Output 部分