Problem:
Score : 200 points

Problem Statement

We have a grid with N rows and M columns of squares. Initially, all the squares are white.

There is a button attached to each row and each column.
When a button attached to a row is pressed, the colors of all the squares in that row are inverted; that is, white squares become black and vice versa.
When a button attached to a column is pressed, the colors of all the squares in that column are inverted.

Takahashi can freely press the buttons any number of times. Determine whether he can have exactly K black squares in the grid.

Constraints

1 \leq N,M \leq 1000

0 \leq K \leq NM

Input

Input is given from Standard Input in the following format:

N M K

Output

If Takahashi can have exactly K black squares in the grid, print Yes; otherwise, print No.

Sample Input 1

2 2 2

Sample Output 1

Yes

Press the buttons in the order of the first row, the first column.

Sample Input 2

2 2 1

Sample Output 2

No

Sample Input 3

3 5 8

Sample Output 3

Yes

Press the buttons in the order of the first column, third column, second row, fifth column.

Sample Input 4

7 9 20

Sample Output 4

No

Solution in Kotlin (1.0.0) (judge verdict: Accepted)

fun main(args: Array<String>) = IO().exec {
    val n = int()
    val m = int()
    val K = int()
    var isOk = false
    for (k in n+1) for (l in m+1) if (k*(m-l)+(n-k)*l==K) isOk = true
    println(if (isOk) "Yes" else "No")
}

// region template
operator fun Int.iterator() = 0.until(this).iterator()

class IO {
    val printable = 33..126
    val buffer = ByteArray(1024)
    var ptr = 0
    var buflen = 0
    val out = java.io.PrintWriter(System.out)
    fun hasNextByte(): Boolean = if (ptr < buflen) true else {
        ptr = 0
        buflen = System.`in`.read(buffer)
        buflen > 0
    }

    fun readByte(): Byte = if (hasNextByte()) buffer[ptr++] else -1
    fun hasNext(): Boolean {
        while (hasNextByte() && buffer[ptr] !in printable) ptr++
        return hasNextByte()
    }

    fun string(): String {
        if (!hasNext()) throw java.util.NoSuchElementException()
        val sb = StringBuilder()
        var b = readByte()
        while (b in printable) {
            sb.appendCodePoint(b.toInt())
            b = readByte()
        }
        return sb.toString()
    }

    fun long(): Long {
        if (!hasNext()) throw java.util.NoSuchElementException()
        var n = 0L
        var minus = false
        var b = readByte()
        if (b == '-'.toByte()) {
            minus = true
            b = readByte()
        }
        if (b !in '0'.toByte()..'9'.toByte()) {
            throw NumberFormatException()
        }
        while (true) {
            if (b in '0'.toByte()..'9'.toByte()) {
                n *= 10
                n += b - '0'.toByte()
            } else if (b == (-1).toByte() || b !in printable) {
                return if (minus) -n else n
            } else {
                throw NumberFormatException()
            }
            b = readByte()
        }
    }

    fun int(): Int {
        val nl = long()
        if (nl !in Integer.MIN_VALUE..Integer.MAX_VALUE) throw NumberFormatException()
        return nl.toInt()
    }

    fun double(): Double = string().toDouble()
    fun print(obj: Any) = out.print(obj)
    fun print(i: Int) = out.print(i)
    fun print(l: Long) = out.print(l)
    fun println(obj: Any) = out.println(obj)
    fun println(i: Int) = out.println(i)
    fun println(l: Long) = out.println(l)
    inline fun exec(block: IO.() -> Unit) {
        block()
        out.flush()
    }
}
// endregion