Migrated from Lutece 339 Non-Decreasing Digits

All parts of this problem, including description, images, samples, data and checker, might be broken. If you find bugs in this problem, please contact the admins.

Description

A number is said to be made up of non-decreasing digits if all the digits to the left of any digit is less than or equal to that digit. For example, the four-digit number 1234 is composed of digits that are non-decreasing. Some other four-digit numbers that are composed of non-decreasing digits are 0011, 1111, 1112, 1122, 2223. As it turns out, there are exactly 715 four-digit numbers composed of non-decreasing digits.

Notice that leading zeroes are required: 0000, 0001, 0002 are all valid four-digit numbers with nondecreasing digits.

For this problem, you will write a program that determines how many such numbers there are with a specified number of digits.

Input

The first line of input contains a single integer $P$, ($1\leq P\leq 1000$), which is the number of data sets that follow. Each data set is a single line that contains the data set number, followed by a space, followed by a decimal integer giving the number of digits $N$, ($1\leq N\leq 64$).

Output

For each data set there is one line of output. It contains the data set number followed by a single space, followed by the number of $N$ digit values that are composed entirely of non-decreasing digits.

Samples

3
1 2
2 3
3 4

1 55
2 220
3 715

Resources

Greater New York 2010