Broadcast Tower

Time limit2sMemory limit512 MB

Summary

Place a tower of height H in a row of buildings; a building west of it receives its signal if no taller building blocks the path. Maximize receivers.

Level: Medium5 of 10
Topics: Stack, Array
Solved: No attempts yet

Problem

City X has $N$ buildings standing in one row from west to east. The westmost building is number 1 and the eastmost is number $N$ . The heights are integers $h_1, h_2, \dots, h_N$ , and no two buildings have the same height. The city government plans to build one broadcast tower in the same row. The tower can stand west of building 1, between two neighbouring buildings, or east of building $N$ . Its height is $H$ , and $H$ differs from every building height.

Because of an unusual design, the tower sends signals only to the west. A signal is a horizontal ray that travels parallel to the ground, and rays leave the whole body of the tower, from the top down to the bottom. The tower therefore emits a continuous band of rays whose width equals the height of the tower. A ray stops where it hits a building. Each building has a receiver on its roof, and a building receives the message if at least one ray reaches that receiver.

In other words, building $i$ receives the message exactly when all three conditions hold: building $i$ stands west of the tower, $h_i$ is not greater than the height of the tower, and no building $j$ with $j > i$ standing between building $i$ and the tower is higher than building $i$ .

In the figure above the buildings that receive the message are 2, 5, 6, and 9.

You are given the heights of the buildings and the height of the tower. Write a program that places the tower where the largest number of buildings receives the message, and prints that number.

Input

The first line contains the number of buildings $N$ and the height of the tower $H$ , separated by a space.

The second line contains the heights of the $N$ buildings, separated by spaces, in order from building 1 to building $N$ .

Output

Print on one line the largest number of buildings that receive the message when the tower is placed in the best position.

Constraints

$1 \le N \le 1000000$
$1 \le h_i \le 10^9$ , $1 \le H \le 10^9$
The building heights are pairwise different, and $H$ equals none of the $h_i$

Explanation

In the first example the best position for the tower is between building 8 and building 9. Buildings 2, 5, 6, 7, and 8 receive the message.

Examples4

Example 1

Input

12 180
200 170 130 90 150 140 40 30 100 160 50 110

Expected output

Example 2
Input
```
1 10
3
```
Expected output
```
1
```
Example 3
Input
```
1 5
7
```
Expected output
```
0
```
Example 4
Input
```
5 100
1 2 3 4 5
```
Expected output
```
1
```