Omgillas

Recent excavations have discovered the rests of an extincted race of pseudo-human primates called Omgillas (not to mistake for gorillas). Among other curiosities, they eated raw fish, slept at least twelve hours a day, and shaved their heads twice a year.

On the other hand, they must knew some basic mathematics, since they used coins with prime values: 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. This strange choice (for instance, there was no way to buy something of value 1 without change) and the fact that Omgillas were a bit silly caused a lot of confusion and their eventual extintion.

The sistem of coins of Omgillas is original enough to be investigated. Unfortunately, current humans are not much more intelligent. Therefore, a program that helps with this task would be welcome. Take into account that the coins were quite big and heavy, so only a few could be used in each transaction. It is known that the strongest Omgilla, the mythical warrior Obok-Aman, was able to carry just 20 coins.

To sumarize: Write a program such that, given a number of coins $c$ and a value $v$ , prints the number of different ways to get an amount of $v$ with exactly $c$ coins. Assume an infinite suply of coins of every kind: 2, 3, 5, …, 29.

Input

Input begins with the number of cases $n$ , followed by $n$ pairs of natural numbers $c$ and $v$ . Assume $1 \le c \le 20$ and $1 \le v \le 10^6$ .

Output

For every case, print the number of different ways to get a value $v$ with exactly $c$ coins.

Problem information

Author: Salvador Roura

Generation: 2026-01-25T10:13:50.128Z