Hindley Street is the place to be if you're after clubs, bars, and live music. It's also a great place to see your typical bar fight.

Each bar is numbered from ~1~ to ~n~. Every night, Channel 9 News dutifully reports the number of fights that break out at each bar. This can take hours, and as a Hindley Street local, you're getting sick of it!

So, you call Channel 9 to complain. Shockingly, they fire back!

"Think you can do better? Prove it!"

Just like that, they invite you to take over crime reporting for the night. But, you've got a plan. Instead of listing the number of fights at every bar, you'll report only the "high-crime" zones: continuous stretches of bars where the number of fights are at least ~k~.

Say ~k = 3~, and the fight counts look like:

1 3 5 6 2 3 7 1 2 1

The "high-crime" zones here are bars ~2~ through ~4~, and bars ~6~ through ~7~. You'd report them as:

2 4
6 7

Do you have what it takes? It's time to knock Channel 9's socks off!

Input

The first line contains two integers, ~n~ ~(1 \leq n \leq 10^5)~, the number of bars on Hindley street, and ~k~ ~(1 \leq k \leq 10^9)~ the number of fights required in a bar to be included in your news report.

The next lines contain ~n~ integers, ~F_i~ ~(1 \leq F_i \leq 10^9)~, the number of fights that break out at each of the bars ~1~ to ~n~.

Output

Report all the ranges of bars with at least ~k~ fights. Ranges should be in sorted order and each range should be printed on its own line.

Clarifications

• At least 1 bar will have at least ~k~ fights.

Example

Input 1

5 4
1 5 2 4 9

Output 1

2 2
4 5

Bars ~2~, ~4~ and ~5~ have at least ~4~ fights. These can be summarised into two ranges.

Input 2

12 15
15 20 25 30 10 10 20 25 10 15 15 15

Output 2

1 4
7 8
10 12

Input 3

10 1
1 1 1 1 1 1 1 1 1 1

Output 3

1 10