How to find out if it is possible to contruct a binary matrix with given row and column sums.

Input :

The first row of input contains two numbers 1≤m,n≤1000, the number of rows and columns of the matrix. The next row contains m numbers 0≤ri≤n – the sum of each row in the matrix. The third row contains n numbers 0≤cj≤m – the sum of each column in the matrix.

Output:

Output “YES” if there exists an m-by-n matrix A, with each element either being 0 or 1. Else "NO".

I tried reading about Tomography algorithms but could not figure out an answer as all the papers related to Tomography algorithm is very complicated.

Can someone please help me..