codeforces#P1932G. Moving Platforms

    ID: 34430 远端评测题 3000ms 512MiB 尝试: 0 已通过: 0 难度: (无) 上传者: 标签>graphsmathnumber theoryshortest paths

Moving Platforms

Description

There is a game where you need to move through a labyrinth. The labyrinth consists of $n$ platforms, connected by $m$ passages.

Each platform is at some level $l_i$, an integer number from $0$ to $H - 1$. In a single step, if you are currently on platform $i$, you can stay on it, or move to another platform $j$. To move to platform $j$ they have to be connected by the passage, and their levels have to be the same, namely $l_i = l_j$.

After each step, the levels of all platforms change. The new level of platform $i$ is calculated as $l'_i = (l_i + s_i) \bmod H$, for all $i$.

You start on platform $1$. Find the minimum number of steps you need to get to platform $n$.

The first line of input contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then the descriptions of the test cases follow.

The first line of each test case contains three integers $n$, $m$, and $H$ ($2 \le n \le 10^5$, $1 \le m \le 10^5$, $1 \le H \le 10^9$).

The second line contains $n$ integers $l_i$, the initial level of each platform ($0 \le l_i \le H-1$).

The third line contains $n$ integers $s_i$, the change of level for each platform ($0 \le s_i \le H-1$).

Next $m$ lines contain a description of the passages. Each passage is described as a pair of integers — the platforms, connected by the passage. There is at most one passage connecting each pair of platforms, and there is no passage connecting a platform to itself.

The sum of $n$ for all tests does not exceed $10^5$, the sum of $m$ for all tests does not exceed $10^5$.

For each test case, print a single integer, the minimum number of steps needed to get from platform $1$ to platform $n$.

If it is impossible to get to platform $n$, print $-1$.

Input

The first line of input contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then the descriptions of the test cases follow.

The first line of each test case contains three integers $n$, $m$, and $H$ ($2 \le n \le 10^5$, $1 \le m \le 10^5$, $1 \le H \le 10^9$).

The second line contains $n$ integers $l_i$, the initial level of each platform ($0 \le l_i \le H-1$).

The third line contains $n$ integers $s_i$, the change of level for each platform ($0 \le s_i \le H-1$).

Next $m$ lines contain a description of the passages. Each passage is described as a pair of integers — the platforms, connected by the passage. There is at most one passage connecting each pair of platforms, and there is no passage connecting a platform to itself.

The sum of $n$ for all tests does not exceed $10^5$, the sum of $m$ for all tests does not exceed $10^5$.

Output

For each test case, print a single integer, the minimum number of steps needed to get from platform $1$ to platform $n$.

If it is impossible to get to platform $n$, print $-1$.

3
3 3 10
1 9 4
2 3 0
1 2
3 2
1 3
2 1 10
1 2
4 6
1 2
8 7 25
22 14 5 3 10 14 11 1
9 5 4 10 7 16 18 18
2 8
6 3
3 5
7 5
2 6
1 4
4 7
6
-1
52

Note

This is how levels of the platforms change, and what actions we need to perform in the first example.

Platform 1Platform 2Platform 3Action
Step 1194Stay on the platform 1
Step 2324Stay on the platform 1
Step 3554Move to the platform 2
Step 4784Stay on the platform 2
Step 5914Stay on the platform 2
Step 6144Move to the platform 3