Wine Tasting

There are $N$ vineyards arranged in a row, numbered from $0$ to $N-1$. Giorgio starts the tour from vineyard $L$, once the first tasting is over he will move on to the vineyard $L+1$, then to the vineyard $L+2$ and so on until he reaches the vineyard $R$. Note that Giorgio can start and end his tour on the same vineyard.

To visit the vineyard $i$ Giorgio has to pay $V_i$ euro. The cost of a tour is the cost of each vineyard visited.

There are a total of $\frac{N \cdot (N+1)}{2}$ different tours, Giorgio will choose one of the tours in the following way:

First, he sorts the tours in ascending order of cost, in case of a tie, the tours with the smallest starting vineyard come first. Then, he chose the $K$-th tour from this order.

Help Giorgio find the first and the last vineyards of the $K$-th tour!

Input data

The first line of the input contains the integers $N$ and $K$. The second line contains $N$ integers $V_i$.

Output data

The output contains a single line which has the integers $L$ and $R$: the first and the last vineyards of Giorgio's tour.

Constraints and clarifications

• $1 \leq N \leq 2 \cdot 10^5$
• $1 \leq K \leq \frac{N \cdot (N+1)}{2}$
• $1 \leq V_i \leq 10^9$
• For tests worth $50$ points, $V_i$ = $1$ for all values in the input.
• For tests worth $20$ more points, $1 \leq N \leq 1000$.

Example 1

stdin

4 4
1 2 3 1

stdout

0 1

Explanation

In the first sample case there are $10$ possible tours, in order:

from $0$ to $0$: the cost is $1$
from $3$ to $3$: the cost is $1$
from $1$ to $1$: the cost is $2$
from $0$ to $1$: the cost is $1+2=3$
from $2$ to $2$: the cost is $3$
from $2$ to $3$: the cost is $3+1=4$
from $1$ to $2$: the cost is $2+3=5$
from $0$ to $2$: the cost is $1+2+3=6$
from $1$ to $3$: the cost is $2+3+1=6$
from $0$ to $3$: the cost is $1+2+3+1=7$

The fourth tour starts from vineyard $0$ and end in vineyard $1$.

Example 2

stdin

6 18
1 2 1 2 1 2

stdout

2 5