AC java 0.14 =

for (int i=0; i<R; i++) {
 int retcode = s(i);
 if (retcode==-1) {
  i=-1;
 }
}

int s(int row) {
 ..
  //some backtracking call bt(list_of_added, left, r)
 ..
 if (errorwith_this_row) {//error row will be processed first, reprocess all rows
  int reg = L[r];
  for (int i=r; i>0; i--) {
   L[i]=L[i-1];
  }
  L[0]=reg;
  return -1;
 }
 ..
 return 0;
}

bt(list_of_added, left, r) {
 if (list_of_added.size=0) return -1;
 index=list_of_added.removelast
 left+=l[index];
 //greedy adding itemd to list_of_added, decrease 'left'

 if (left>0) bt(list_of_added, left, r);

}

also i use marked[] with indexes of rows were needed,
i use Lorig[], L[] (sorted Lorig[]) and id[], and ID[] (indexes of original lengths in Lorig)