Blocked Stairs - Repovive Starter Round 1 | Repovive

7B. Blocked Stairs

1000 pts1s256 MB

You are given a staircase with stairs numbered from $0$ to $m$ .

Initially, you are standing on stair $0$ , and you want to reach stair $m$ .

Some stairs are blocked. The blocked stairs are $a_1, a_2, \ldots, a_n$ . You can make jumps of length $1$ or $2$ . After each jump, you must not land on a blocked stair.

Determine whether it is possible to reach stair $m$ .

Constraints

$2 \le m \le 10^9$
$1 \le n \le 2 \times 10^5$
$1 \le a_i < m$
All $a_i$ are distinct.

Input

m \quad n

a_1 \quad a_2 \quad \cdots \quad a_n

Output

Print Yes if it is possible to reach stair $m$ , and No otherwise.

Samples

Input

5 2
2 4

Explanation

One valid route is $0 \to 1 \to 3 \to 5$ .

Output

Yes

Input

5 2
2 3

Explanation

Stairs $2$ and $3$ are both blocked. After reaching stair $1$ , both possible next landings are blocked.

Output

No

You are given a staircase with stairs numbered from $0$ to $m$ .

Initially, you are standing on stair $0$ , and you want to reach stair $m$ .

Some stairs are blocked. The blocked stairs are $a_1, a_2, \ldots, a_n$ . You can make jumps of length $1$ or $2$ . After each jump, you must not land on a blocked stair.

Determine whether it is possible to reach stair $m$ .

$2 \le m \le 10^9$
$1 \le n \le 2 \times 10^5$
$1 \le a_i < m$
All $a_i$ are distinct.

m \quad n

a_1 \quad a_2 \quad \cdots \quad a_n

Print Yes if it is possible to reach stair $m$ , and No otherwise.

One valid route is $0 \to 1 \to 3 \to 5$ .

Stairs $2$ and $3$ are both blocked. After reaching stair $1$ , both possible next landings are blocked.

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7B. Blocked Stairs

Constraints

Input

Output

Samples

7B. Blocked Stairs

Constraints

Input

Output

Samples