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
ayushgupta1997: 2019-02-11 18:28:41

start from the left most digit, and try and build the possible recursion tree of possibilities, you will find a pattern then, turn the pattern into a 2D dp, precomputation matrix.

Last edit: 2019-02-11 18:29:10
sauravraj62: 2018-11-10 06:03:31

why so weird output format... it costs 2 WA!!!

jmr99: 2018-10-30 08:43:20

1.'spoiler' will do the job
2. formula will also do the job

ankit1cool: 2018-06-14 14:39:54

Remember to use long long costed me 1wa

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 :)

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.


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