Can Sort Permutation in Given Moves

Each step swaps two distinct indices. For each moves value, decide whether the permutation can become ascending in exactly that many steps, and output a 01 string.

输入格式

The first line contains n q (1..100000); the second line contains a permutation of 1..n; the third line contains q moves values (1..10⁹).

输出格式

Output a 01 string of length q.

样例 1

输入：

4 2
2 3 1 4
2 3

输出：

10

样例 2

输入：

5 3
4 5 1 3 2
1 2 3

输出：

001

样例 3

输入：

1 2
1
1 2

输出：

00

样例说明

Example 1: at least 2 steps are needed; 2 is feasible while 3 has the wrong parity, so output 10. Example 2: one 3-cycle and one 2-cycle need at least 3 steps, so output 001; the source's 011 wrongly treats two steps as feasible. Example 3: there is only one index, so no step can be performed; output 00.