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
spojabhi: 2017-12-17 17:18:10

"OEIS" best site for getting sequences.

vishesh197: 2017-09-26 15:04:03

simple problem.... just use dp and long long and state of dp as dp(last digit chosen,number of digits).AC in 1st go...

code_aim: 2017-09-04 15:52:59

100th

quantic: 2017-07-01 18:27:51

wow.. a good combinatorics problem!.. pure maths :)

imperfectboy: 2017-06-08 13:18:00

use long long !!! Happy DP :)

da_201501181: 2017-06-06 09:35:52

Easy AC in one GO..!! O(n*10) java- 0.04s

cj23897: 2017-06-03 08:32:48

Easy dp. Just think for 20 minutes and write if you are not getting.

abdulaziz1997: 2017-04-12 16:38:33

I'm a beginner in dp , so I do it quickly with number theory ...
Even though , I got 1 WA for presentation =(.

Last edit: 2017-04-12 16:38:56
nilabja16180: 2017-03-20 10:51:48

Easy dp, AC IN ONE GO!

sonudoo: 2017-01-29 17:51:02

The series is the 10th row of Pascal's triangle. Too easy in number theory


Added by:John Mario
Date:2011-03-22
Time limit:0.166s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:ACM Greater New York Regionals 2010