Problem Statement

We have a playlist with $N songs numbered 1, \dots, N$.
Song i lasts A_i seconds.
When the playlist is played, song $1, song 2, \ldots$, and song N play in this order. When song N ends, the playlist repeats itself, starting from song 1 again. While a song is playing, the next song does not play; when a song ends, the next song starts immediately.
At exactly T seconds after the playlist starts playing, which song is playing? Also, how many seconds have passed since the start of that song?
There is no input where the playlist changes songs at exactly T seconds after it starts playing.

Input

The input is given from Standard Input in the following format:
N T
$A_1 \ldots A_N$

Output

Print an integer representing the song that is playing at exactly T seconds after the playlist starts playing, and an integer representing the number of seconds that have passed since the start of that song, separated by a space.

Constraints

• $1 \leq N \leq 10^5$
• $1 \leq T \leq 10^{18}$
• $1 \leq A_i \leq 10^9$
• The playlist does not change songs at exactly T seconds after it starts playing.
• All values in the input are integers.

Sample Input 1

3 600
180 240 120

Sample Output 1

1 60

When the playlist is played, the following happens. (Assume that it starts playing at time 0.)

• From time 0 to time 180, song 1 plays.
• From time 180 to time 420, song 2 plays.
• From time 420 to time 540, song 3 plays.
• From time 540 to time 720, song 1 plays.
• From time 720 to time 960, song 2 plays.
• $\qquad\vdots$

At time 600, song 1 is playing, and 60 seconds have passed since the start of that song.

Sample Input 2

3 281
94 94 94

Sample Output 2

3 93

Sample Input 3

10 5678912340
1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000

Sample Output 3

6 678912340

见题面 Input 部分

见题面 Output 部分