#935 Pepero Packing

Statement

Statement language

There are $N$ Pepero sticks in a row with weights $A_1,A_2,\ldots,A_N$ . A box contains a nonempty contiguous segment whose total weight is at least $X$ . Each stick may belong to at most one box, and sticks may be left unused. Maximize the number of boxes, then minimize the total number of used sticks among all ways attaining that maximum. If no box can be made, both values are $0$ .

Input

The input is given in the following format:

$N\ X$ $A_1\ A_2\ \cdots\ A_N$

Output

Print the maximum number of boxes and the minimum total number of used sticks among arrangements attaining that maximum, separated by a space.

Constraints

$1 \leq N \leq 200\ 000$ .
$1 \leq X \leq 10^{18}$ .

Subtasks

#	Score	Constraints
1	30	$N \leq 2000$ .
2	70	No additional constraints.

Samples

Sample 1

Input

2 2
1 2

Output

1 1

Sample 2

Input

6 6
4 3 3 6 1 6

Output

3 4

Sample 3

Input

3 10
1 2 3

Output

0 0