NY10E - Non-Decreasing Digits


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 non-decreasing 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 ≤ P ≤ 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 ≤ N ≤ 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.

Example

Input:
3
1 2
2 3
3 4

Output:
1 55
2 220
3 715

hide comments
satya_jha123: 2015-08-29 15:31:49

form a dp table to understand this its good for beginners

ABHIJEET: 2015-07-29 23:16:54

simple accepted in n*n*n

ihak: 2015-07-27 17:02:00

Easy Digit DP with no constraints :) . Can be solved by math too.
But a better version will be simply the number of such numbers between A and B .

SangKuan: 2015-07-04 05:33:42

math...

Shashank Tiwari: 2015-07-01 00:40:53

@aman ; those 1,2,3 are test cases and not n .
Hence , the output is correct.

Ankush : 2015-06-23 20:38:01

An easy one, AC in one go ;)

Aman: 2015-02-01 06:08:22

note: the given ans is wrong...
correct one is this:
3
1 10
2 55
3 220
it cost me two wrong answer...

Reply (numerix): You are wrong.

Last edit: 2015-02-01 07:56:59

Added by:John Mario
Date:2011-03-22
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:ACM Greater New York Regionals 2010