Problem Statement

There are N ants on a number line, labeled 1 to $N. Ant i (1 \leq i \leq N) starts at coordinate X_i$ and faces either a positive or negative direction. Initially, all ants are at distinct coordinates. The direction each ant is facing is represented by a binary string S of length N, where ant i is facing the negative direction if S_i is 0 and the positive direction if S_i is 1.
Let the current time be 0, and the ants move in their respective directions at a speed of 1 unit per unit time for (T+0.1) units of time until time (T+0.1). If multiple ants reach the same coordinate, they pass through each other without changing direction or speed. After (T+0.1) units of time, all ants stop.
Find the number of pairs (i, j) such that $1 \leq i < j \leq N$ and ants i and j pass each other from now before time (T+0.1).

Input

The input is given from Standard Input in the following format:
N T
S
X_1 X_2 ... X_N

Output

Print the answer.

Constraints

• $2 \leq N \leq 2 \times 10^{5}$
• $1 \leq T \leq 10^{9}$
• S is a string of length N consisting of 0 and 1.
• -$10^{9} \leq X_i \leq 10^{9} (1 \leq i \leq N)$
• $X_i \neq X_j (1 \leq i < j \leq N)$
• N, T, and $X_i (1 \leq i \leq N)$ are integers.

Sample Input 1

6 3
101010
-5 -1 0 1 2 4

Sample Output 1

5

The following five pairs of ants pass each other:

• Ant 3 and ant 4 pass each other at time 0.5.
• Ant 5 and ant 6 pass each other at time 1.
• Ant 1 and ant 2 pass each other at time 2.
• Ant 3 and ant 6 pass each other at time 2.
• Ant 1 and ant 4 pass each other at time 3.

No other pairs of ants pass each other, so print 5.

Sample Input 2

13 656320850
0100110011101
-900549713 -713494784 -713078652 -687818593 -517374932 -498415009 -472742091 -390030458 -379340552 -237481538 -44636942 352721061 695864366

Sample Output 2

14

见题面 Input 部分

见题面 Output 部分