Problem B
Beautiful Subarrays

The Great Lord Pooty has an array of numbers $A$ and a special number $K$. $A$ is $0$-indexed, i.e. the first element has index $0$, the second has index $1$, and so on. By decree, he defined the beauty of a subarray as the sum of its value minus $K$ multiplied by its length. Formally, for some integers $0\le L\le R\le N-1$, if we have the subarray $A[L\dots R]$, we define $\text{Beauty}(L,R)=\sum _L^R(A_i)-(R-L+1)\times K$.

Today, he wants to find a subarray with some beauty $B$. As such it falls to you, his humble servant, to find such a subarray if it exists, or face his eternal wrath.

Input

The first line contains three integers, $N(1\le N\le 200000)$, $K(0\le K\le 200000)$ and $B(-{10}^{13}\le B\le {10}^{13})$. The second line prints the $0$-based indexed array $A$ which is given by $N$ integers $(-200000\le A_i\le 200000)$.

Output

If such a subarray exists, print $L$ and $R$, the leftmost and rightmost index of the subarray, else print $-1$. If multiple subarray exist, print the smallest $(L,R)$ lexicographically. This means that we break ties by smallest $L$, followed by smallest $R$.

Subtasks

1. ($25$ Points): $N\le 200$.

2. ($15$ Points): $N\le 3000,K=0$

3. ($10$ Points): $N\le 3000$

4. ($10$ Points): $K=0$ and for all $0\le i\le N-1$, $0\le A_i$

5. ($10$ Points): For all $0\le i\le N-1$, $K\le A_i$

6. ($10$ Points): $K=0$

7. ($20$ Points): No additional constraint.

Explanation

In the first sample, either $(0,1)$, $(1,2)$, and $(2,3)$ are possible subarrays with beauty $B=5$ (as $K=0$). We print the lexicographically smallest subarray: $(0,1)$.

In the second sample, $(1,3)$ is the only possible subarray with beauty $B=5$ as $A_1+A_2+A_3-(3-1+1)\times K=3+2+3-(3-1+1)\times 1=8-3=5$.

In the third sample, there is no such a subarray, so we print $-1$.

Warning

The I/O files are large. Please use fast I/O methods.

4 0 5
3 2 3 2

0 1

4 1 5
2 3 2 3

1 3

1 3 9
13

-1