Yet Another Problem

1000ms

262144K

Description:

You are given an array $$$a$$$ of $$$n$$$ integers $$$a_1, a_2, a_3, \ldots, a_n$$$.

You have to answer $$$q$$$ independent queries, each consisting of two integers $$$l$$$ and $$$r$$$.

Consider the subarray $$$a[l:r]$$$ $$$=$$$ $$$[a_l, a_{l+1}, \ldots, a_r]$$$. You can apply the following operation to the subarray any number of times (possibly zero)-
1. Choose two integers $$$L$$$, $$$R$$$ such that $$$l \le L \le R \le r$$$ and $$$R - L + 1$$$ is odd.
2. Replace each element in the subarray from $$$L$$$ to $$$R$$$ with the XOR of the elements in the subarray $$$[L, R]$$$.
The answer to the query is the minimum number of operations required to make all elements of the subarray $$$a[l:r]$$$ equal to $$$0$$$ or $$$-1$$$ if it is impossible to make all of them equal to $$$0$$$.

You can find more details about XOR operation here.

Input:

The first line contains two integers $$$n$$$ and $$$q$$$ $$$(1 \le n, q \le 2 \cdot 10^5)$$$ — the length of the array $$$a$$$ and the number of queries.

The next line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ $$$(0 \le a_i \lt 2^{30})$$$ — the elements of the array $$$a$$$.

The $$$i$$$-th of the next $$$q$$$ lines contains two integers $$$l_i$$$ and $$$r_i$$$ $$$(1 \le l_i \le r_i \le n)$$$ — the description of the $$$i$$$-th query.

Output:

For each query, output a single integer — the answer to that query.

Sample Input:

7 6
3 0 3 3 1 2 3
3 4
4 6
3 7
5 6
1 6
2 2

Sample Output:

Note:

In the first query, $$$l = 3, r = 4$$$, subarray = $$$[3, 3]$$$. We can apply operation only to the subarrays of length $$$1$$$, which won't change the array; hence it is impossible to make all elements equal to $$$0$$$.

In the second query, $$$l = 4, r = 6$$$, subarray = $$$[3, 1, 2]$$$. We can choose the whole subarray $$$(L = 4, R = 6)$$$ and replace all elements by their XOR $$$(3 \oplus 1 \oplus 2) = 0$$$, making the subarray $$$[0, 0, 0]$$$.

In the fifth query, $$$l = 1, r = 6$$$, subarray = $$$[3, 0, 3, 3, 1, 2]$$$. We can make the operations as follows:

Choose $$$L = 4, R = 6$$$, making the subarray $$$[3, 0, 3, 0, 0, 0]$$$.
Choose $$$L = 1, R = 5$$$, making the subarray $$$[0, 0, 0, 0, 0, 0]$$$.

Informação

Provedor Codeforces

Código CF1747D