N-dimensional travel

Subin likes to travel. With nowhere left to go on Earth, Subin sets off into an N-dimensional universe. A point of this universe is written as N coordinates, and the coordinates are indexed from 1 to N.

Subin starts at the origin, the point whose every coordinate is 0, and each move takes two steps.

• Choose the index of the coordinate to move, one of 1 to N.
• Move to the point where that coordinate is 1 larger or 1 smaller. Every other coordinate stays as it was before the move.

Before leaving, Subin wrote down a travel plan. The plan lists, in order, the coordinate index chosen for each move and whether the move increases or decreases that coordinate.

Write a program that follows the plan and prints 1 if every point, including the starting point and the last point, is visited exactly once, and 0 if some point is visited two or more times.

The first line contains the number of dimensions $N$. ($1 \le N \le 10^9$)

The second line contains the length $M$ of the travel plan. ($1 \le M \le 50$)

The third line contains the $M$ coordinate indices chosen in the plan, in move order, separated by spaces. Each index is between $1$ and $N$.

The fourth line contains a string of length $M$. If its $i$-th character is +, the $i$-th move increases the coordinate by 1, and if it is -, the move decreases the coordinate by 1.

Print 1 if every point is visited exactly once, and 0 otherwise.

In two dimensions, choosing indices 1, 2, 1, 2 with directions +, +, -, - moves along $(0,0) \to (1,0) \to (1,1) \to (0,1) \to (0,0)$, so $(0,0)$ is visited twice.

In three dimensions, choosing indices 1, 2, 3, 1, 2 with directions +, +, +, -, - moves along $(0,0,0) \to (1,0,0) \to (1,1,0) \to (1,1,1) \to (0,1,1) \to (0,0,1)$, and no point is visited twice.