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
prateek1985: 2016-02-27 13:07:44

Awesome problem for dp beginners :)

abc_c: 2016-02-11 14:41:54

Too Easy...
Nice Problem...AC in 1st go!!!

Akshay Damle: 2016-01-27 22:54:45

30 sec to debug and then AC in 1 go :D

BRAIN: 2015-12-31 14:05:09

O(P + 65 * 9) is enough !

kapoor_adhish: 2015-12-17 12:33:38

AC in first go!!
nice one..

subhstar: 2015-11-14 22:33:15

first dp without any help.. :)

Ravi: 2015-10-22 21:11:27

DP + precomputation and solved in 0.0 :)

topke: 2015-10-22 11:51:11

Use long long

twist akid sultan: 2015-10-09 20:28:29

An easy dp.... can be solved by direct formula too.

just_code21: 2015-09-25 19:28:45

O(10*n)...easy one...


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