Tanya and Toys

Source: Codeforces

Version: Phuoc Hung OJ Extended

Problem Statement

Toy types are numbered by positive integers, and type $i$ costs $i$. Tanya already owns $n$ distinct types $a_i$ and has budget at most $m$. Buy as many new distinct types as possible, never buying a type already owned. If several optimal sets exist, any valid optimal set may be printed.

Input

The first line contains $n,m$. The second line contains $n$ distinct integers $a_i$.

Output

The first line prints $k$. The second line prints $k$ distinct selected type indices in any order. If $k=0$, the second line may be empty.

Subtasks

General constraints:

• $1 \le n \le 10^5$.

• $1 \le m \le 10^9$.

• $1 \le a_i \le 10^9$.

• The $a_i$ are pairwise distinct.

• Subtask 1 (20 points): $n \le 20$, $m \le 200$

• Subtask 2 (30 points): $n \le 2000$, $m \le 10^6$

• Subtask 3 (50 points): No additional constraints.

Examples

Input

3 7
1 3 4

Output

2
2 5

Explanation

Type $2$ costs $2$, and the next cheapest missing type is $5$, costing $5$. The total is exactly $7$, so the sample buys two new types.