val     = 1002578;
z       = [19,0,0,0,0,0,0,0,0,0,0,0,0,37,0,0,0,0,0,751,0,29,0,0,0,0,0,0,0,0,0,0,13,0,0,0,0,0,0,0,0,0,23,0,0,0,0,0,0,0,431,0,0,0,0,0,0,0,0,0,41,0,0,0,0,0,0,17];
idxz    = find(z>0);
z       = z(z>0);

%Part A
idx = 1;
while 1
    if any(mod(val+idx,z)==0)
        disp(z(find(mod(val+idx,z)==0))*idx)
        break
    end
    idx=idx+1;
end

%Part B
val = prod(z); % Upper bound
while 1
    if mod(val,z(1))==0
        if mod(val+idxz(2)-1,z(2))==0
            if mod(val+idxz(3)-1,z(3))==0
                if mod(val+idxz(4)-1,z(4))==0
                    if mod(val+idxz(5)-1,z(5))==0
                        if mod(val+idxz(6)-1,z(6))==0
                            if mod(val+idxz(7)-1,z(7))==0
                                if mod(val+idxz(8)-1,z(8))==0
                                    if mod(val+idxz(9)-1,z(9))==0
                                        val
                                        break
                                    end
                                else
                                    val = val - prod(z(1:7));
                                    continue
                                end
                            else
                                val = val - prod(z(1:6));
                                continue
                            end
                        else
                           val = val - prod(z(1:5));
                            continue
                        end
                    else
                        val = val - prod(z(1:4));
                        continue
                    end
                else
                    val = val - prod(z(1:3));
                    continue
                end
            else
                val = val - prod(z(1:2));
                continue
            end
        else
            val = val - z(1);
            continue
        end
    else
        val = val-mod(val,z(1));
        continue
    end
    val=val-1;
end