# Problem C

Tomography

Binary tomography deals with the problem of reconstructing binary images from a small number of projections. One of its most basic problems is to construct a binary ($\{ 0,1\} $-valued) matrix with given row and column sums. This is not always possible and your task is to determine when it is.

## Input

The first line of input contains two numbers $1\leq m,n\leq 1000$, the number of rows and columns of the matrix. The next line contains $m$ numbers $0\leq r_ i\leq n$ – the sum of each row in the matrix. The third line contains $n$ numbers $0\leq c_ j\leq m$ – the sum of each column in the matrix.

## Output

Output “`Yes`” if there exists an $m$-by-$n$ matrix $\mathbf{A}$, with each element either
beeing 0 or 1, such that

Otherwise output “`No`”.

## Example

The figure below illustrates a matrix with the row and column sums of sample input 1.

Sample Input 1 | Sample Output 1 |
---|---|

3 4 2 3 2 1 1 3 2 |
Yes |

Sample Input 2 | Sample Output 2 |
---|---|

3 3 0 0 3 0 0 3 |
No |