Problem7120--ABC271 —— Ex - General General

7120: ABC271 —— Ex - General General

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Time Limit : 1.000 sec  Memory Limit : 256 MiB

Description

Solve the following problem for $T$ test cases.
A piece is placed at the origin (0, 0) on an xy-plane. You may perform the following operation any number of (possibly zero) times:
  • Choose an integer i such that $1 \leq i \leq 8$ and $s_i=1$. Let (x, y) be the current coordinates where the piece is placed.
    • If $i=1$, move the piece to (x+1,y).
    • If $i=2$, move the piece to (x+1,y+1).
    • If $i=3$, move the piece to (x,y+1).
    • If $i=4$, move the piece to (x-1,y+1).
    • If $i=5$, move the piece to (x-1,y).
    • If $i=6$, move the piece to (x-1,y-1).
    • If $i=7$, move the piece to (x,y-1).
    • If $i=8$, move the piece to (x+1,y-1).
Your objective is to move the piece to (A, B).
Find the minimum number of operations needed to achieve the objective. If it is impossible, print -1 instead.

Input

The input is given from Standard Input in the following format:
$T$
$\mathrm{case}_1$
$\mathrm{case}_2$
$\vdots$
$\mathrm{case}_T$

Here, $\mathrm{case}_i$ denotes the i-th test case.
Each test case is given in the following format:
$A\ B\ s_1s_2s_3s_4s_5s_6s_7s_8$

Output

Print $T$ lines in total.
The $i$-th line should contain the answer to the $i$-th test case.

Constraints

$1≤T≤10^4$
$-10^9 \leq A,B \leq 10^9$
$s_i$ is 0 or 1.
$T,A$, and $B$ are integers.

Sample 1 Input

7
5 3 10101010
5 3 01010101
5 3 11111111
5 3 00000000
0 0 11111111
0 1 10001111
-1000000000 1000000000 10010011

Sample 1 Output

8
5
5
-1
0
-1
1000000000

Source/Category