As you have known MMM corporation lab researches the matter of haricot proportions in soup For every day. As we wrote in the previous problem (T) the ladle is placed down into the soup pan. But now we are not interested in the form and linear sizes of the ladle. This time the ladle holds exactly M haricot seeds of N got into the pan. All the seeds are of different size.
Experimenters calculate the quantity of possible methods to proportion M seeds in the pan. Requisite quantity of methods is calculated with the formula: C = N!/(M!·(N−M)!). The main feature of these experiments is the quantity of different prime divisors of number C.
Example. N = 7, M = 3. C = 7!/(3!*4!) = 5040/(6*24) = 35 = 5*7. This example shows that the quantity of different prime divisors is 2.
Lest money would be spent for programmer, MMM corporation board decided to make necessary estimating during trial tour of quarterfinal world programming contest in Rybinsk.
Thus, your aim is to find the quantity of different prime divisors of number C.
Input contains integers N and M.
You may assume that 1 ≤ M < N ≤ 50000.
Output should contain one integer.
Источник задачи: Rybinsk State Avia Academy