Uolevi is attempting to land a rocket ship on the moon. He can see n meters directly ahead of him through the ship's tiny window. The height of the moon's surface i meters ahead of the ship is a_i mm. Due to budget cuts, the ship has no landing gear and cannot tolerate height differences greater than x mm beneath it when landed. Help Uolevi find the longest strip of land ahead of the ship where the height difference between the highest and lowest points is no more than x. Report its position and length.

Input

The first line contains two integers n and x.

The second line contains n integers a_1,\,a_2,\dots,\,a_n.

Output

Print the position and length of the longest strip on a single line. If there are multiple answers, print any.

Constraints

• 1 \leq n \leq 10^5
• 0 \leq a_i \leq 10^9
• 0 \leq x \leq 10^9

Example 1

Input:

10 4
10 7 10 0 1 3 10 1 2 1

Output:

8 3

Example 2

Input:

5 10
9 6 1 10 9

Output:

1 5

Example 3

Input:

1 0
0

Output:

1 1