It's Halloween again! Little sankeeth_ganeswaran goes scaring people in his neighbourhood. Each neighbour he visits has a certain amount of Trehalose (noise tolerance). Some neighbours are easily scared and some are quite fearless! This is very sad for sankeeth_ganeswaran whose voice can only scream ~M~ Trehalose. There are ~N~ houses numbered ~1~ to ~N~. Each house ~h_i~ has a Trehalose tolerance of ~m_i~. Output the largest range of houses sankeeth_ganeswaran can spook in a consecutive row.

Input Specification

The first line contains an integer ~N~, the number of houses followed by ~M~, the amount of Trehalose sankeeth_ganeswaran can scream.

The next ~N~ lines will contain the integer ~m_i~ the neighbour's Trehalose tolerance.

Output Specification

On one line, print the integers ~a~ and ~b~ denoting the range of the most consecutive houses Sankeeth can scare (inclusive).

If there is more than one solution, output the first occurrence.

Constraints

For all subtasks:

~1 \le N \le 1\,000\,000~

~1 \le M \le 10\,000~

~1 \le m_i \le M~

Subtask 1 [10%]

~N \le 10~

Subtask 2 [20%]

~N \le 1\,000~

Subtask 3 [70%]

No further constraints.

Sample Input

5 1000
700
300
200
10
850

Sample Output

2 4

Sample Explanation

Starting at house 2 ending at house 4, Sankeeth screams at 3 neighbours using 300 + 200 + 10 trehalose.