Question

Raj, Tia and Paint

5 2 1

Yes

Raj can paint the ribbon as follows: [1,2,1,2,1]. It's impossible to change the color of at most 1 part so that all parts have the same color.

5 2 2

No

No matter how Raj paints the ribbon, Tia will always be able to repaint 2 parts so that all parts have the same color.

Raj and Tia have purchased a ribbon consisting of n segments. They plan to paint it together.

Initially, Raj will paint each segment of the ribbon using one of m available colors. He can freely choose the color for each segment.

Initially, Raj will paint each segment of the ribbon using one of m available colors. He can freely choose the color for each segment.

Then, Tia will choose **at most k** parts of the ribbon and repaint them into the same color (she chooses the affected parts and the color arbitrarily).

Input

Input consists of three space separated integers: n, m, k (1 <= n, m, k <= 30).

Output

Print "Yes" if it's possible, "No" otherwise. (Case sensitive)

Example

**Input 1**

5 2 1

**Output**

Yes

**Explanation**

Raj can paint the ribbon as follows: [1,2,1,2,1]. It's impossible to change the color of at most 1 part so that all parts have the same color.

**Input 2**

5 2 2

**Output**

No

**Explanation**

No matter how Raj paints the ribbon, Tia will always be able to repaint 2 parts so that all parts have the same color.