Table for P1 's journey from  start to meeting cell
for ( int i = 1 ; i <= N ; i ++ ) for ( int j = 1 ; j <= M ; j ++ ) P1S [ i ] [ j ] = max ( P1S [ i - 1 ] [ j ] , P1S [ i ] [ j - 1 ] ) + A [ i - 1 ] [ j - 1 ] ;