## COWCAR - Cow Cars

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N (1 ≤ N ≤ 50,000) cows conveniently numbered 1, ..., N are driving in separate cars along a highway in Cowtopia. Cow i can drive in any of M different high lanes (1 ≤ M ≤ N) and can travel at a maximum speed of Si (1 ≤ Si ≤ 1,000,000) km/hour.

After their other bad driving experience, the cows hate collisions and take extraordinary measures to avoid them. On this highway, cow i reduces its speed by D (0 ≤ D ≤ 5,000) km/hour for each cow in front of it on the highway (though never below 0 km/hour). Thus, if there are K cows in front of cow i, the cow will travel at a speed of max(Si - D*K, 0). While a cow might actually travel faster than a cow directly in front of it, the cows are spaced far enough apart so crashes will not occur once cows slow down as described.

Cowtopia has a minimum speed law which requires everyone on the highway to travel at a a minimum speed of L (1 ≤ L ≤ 1,000,000) km/hour, so sometimes some of the cows will be unable to take the highway if they follow the rules above. Write a program that will find the maximum number of cows that can drive on the highway while obeying the minimum speed limit law.

### Input

The first line contains the four integers N, M, D, and L. For the next N lines, line i+1 contains the integer Si.

### Output

Print a single integer denoting the maximum number of cows that can take the highway.

### Example

```Input:
3 1 1 5
5
7
5

Output:
2
```

We can obtain two cows by putting either cow with speed 5 first and the cow with speed 7 second.