A Diverse Team
There are n students in a school class, the rating of the i-th student on Codehorses is ai. You have to form a team consisting of k students (1≤k≤n) such that the ratings of all team members are distinct.
If it is impossible to form a suitable team, print "NO" (without quotes). Otherwise print "YES", and then print k distinct numbers which should be the indices of students in the team you form. If there are multiple answers, print any of them.
Input
The first line contains two integers n and k (1≤k≤n≤100) — the number of students and the size of the team you have to form.
The second line contains n integers a1,a2,…,an (1≤ai≤100), where ai is the rating of i-th student.
Output
If it is impossible to form a suitable team, print "NO" (without quotes). Otherwise print "YES", and then print k distinct integers from 1 to n which should be the indices of students in the team you form. All the ratings of the students in the team should be distinct. You may print the indices in any order. If there are multiple answers, print any of them.
Assume that the students are numbered from 1 to n.
Examples input
5 3
15 13 15 15 12 output
YES
1 2 5 input
5 4
15 13 15 15 12 output
NO input
4 4
20 10 40 30 output
YES
1 2 3 4 Note
All possible answers for the first example:
{1 2 5}
{2 3 5}
{2 4 5}
Note that the order does not matter.
B Substrings Sort
You are given n strings. Each string consists of lowercase English letters. Rearrange (reorder) the given strings in such a way that for every string, all strings that are placed before it are its substrings.
String a is a substring of string b if it is possible to choose several consecutive letters in b in such a way that they form a. For example, string "for" is contained as a substring in strings "codeforces", "for" and "therefore", but is not contained as a substring in strings "four", "fofo" and "rof".
Input
The first line contains an integer n(1 ≤ n ≤ 100) — the number of strings.
The next nlines contain the given strings. The number of letters in each string is from 1 to 100, inclusive. Each string consists of lowercase English letters. Some strings might be equal.
Output
If it is impossible to reorder n given strings in required order, print "NO" (without quotes). Otherwise print "YES" (without quotes) and n given strings in required order.
Examples input
5
a
aba
abacaba
ba
aba output
YES
a
ba
aba
aba
abacaba input
5
a
abacaba
ba
aba
abab output
NO input
3
qwerty
qwerty
qwerty output
YES
qwerty
qwerty
qwerty Note
In the second example you cannot reorder the strings because the string "abab" is not a substring of the string "abacaba".
C Equal Sums
You are given k sequences of integers. The length of the i-th sequence equals to ni. You have to choose exactly two sequences i and j(i ≠ j) such that you can remove exactly one element in each of them in such a way that the sum of the changed sequence i(its length will be equal to ni−1) equals to the sum of the changed sequence j(its length will be equal to nj−1).
Note that it's required to remove exactly one element in each of the two chosen sequences.
Assume that the sum of the empty (of the length equals 0) sequence is 0.
Input
The first line contains an integer k(2 ≤ k ≤ 2⋅10^5) — the number of sequences.
Then k pairs of lines follow, each pair containing a sequence.
The first line in the i-th pair contains one integer ni(1 ≤ ni < 2⋅10^5) — the length of the i-th sequence.
The second line of the i-th pair contains a sequence of ni integers ai,1, ai,2, …, ai,n i.
The elements of sequences are integer numbers from −104 to 104.
The sum of lengths of all given sequences don't exceed 2⋅10^5, i.e. n1+n2+⋯+nk ≤ 2⋅10^5.
Output
If it is impossible to choose two sequences such that they satisfy given conditions, print "NO" (without quotes). Otherwise in the first line print "YES" (without quotes), in the second line — two integers i, x(1 ≤ i ≤ k, 1 ≤ x ≤ ni), in the third line — two integers j, y(1 ≤ j ≤ k, 1 ≤ y ≤ nj). It means that the sum of the elements of the i-th sequence without the element with index x equals to the sum of the elements of the j-th sequence without the element with index y.
Two chosen sequences must be distinct, i.e. i ≠ j. You can print them in any order.
If there are multiple possible answers, print any of them.
Examples input
2
5
2 3 1 3 2
6
1 1 2 2 2 1 output
YES
2 6
1 2 input
3
1
5
5
1 1 1 1 1
2
2 3 output
NO input
4
6
2 2 2 2 2 2
5
2 2 2 2 2
3
2 2 2
5
2 2 2 2 2 output
YES
2 2
4 1 Note
In the first example there are two sequences
[2, 3, 1, 3, 2] and [1, 1, 2, 2, 2, 1]. You can remove the second element from the first sequence to get [2,
1, 3, 2] and you can remove the sixth element from the second sequence to get [1, 1, 2, 2, 2]. The sums of the both resulting sequences equal to 8, i.e. the sums are equal.
D Points and Powers of Two
There are n distinct points on a coordinate line, the coordinate of i-th point equals to xi. Choose a subset of the given set of points such that the distance between each pair of points in a subset is an integral power of two. It is necessary to consider each pair of points, not only adjacent. Note that any subset containing one element satisfies the condition above. Among all these subsets, choose a subset with maximum possible size.
In other words, you have to choose the maximum possible number of points xi1, xi2, …, xim such that for each pair x
ij, xik it is true that |xij−xik| = 2^d where d is some non-negative integer number (not necessarily the same for each pair of points).
Input
The first line contains one integer n(1 ≤ n ≤ 2⋅10^5) — the number of points.
The second line contains n pairwise distinct integers x1, x2, …, xn(−10^9 ≤ xi ≤10^9) — the coordinates of points.
Output
In the first line print m — the maximum possible number of points in a subset that satisfies the conditions described above.
In the second line print m integers — the coordinates of points in the subset you have chosen.
If there are multiple answers, print any of them.
Examples input
6
3 5 4 7 10 12 output
3
7 3 5 input
5
-1 2 5 8 11 output
1
8 Note
In the first example the answer is [7, 3, 5]. Note, that |7 − 3| = 4 = 2^2, |7 − 5| = 2 = 2^1 and |3 − 5| = 2 = 2^1
. You can't find a subset having more points satisfying the required property.
E Divisibility by 25
You are given an integer n from 1 to 10^18 without leading zeroes.
In one move you can swap any two adjacent digits in the given number in such a way that the resulting number will not contain leading zeroes. In other words, after each move the number you have cannot contain any leading zeroes.
What is the minimum number of moves you have to make to obtain a number that is divisible by 25 ? Print -1 if it is impossible to obtain a number that is divisible by 25.
Input
The first line contains an integer n(1 ≤ n ≤ 10^18). It is guaranteed that the first (left) digit of the number
n is not a zero.
Output
If it is impossible to obtain a number that is divisible by 25, print -1. Otherwise print the minimum number of moves required to obtain such number.
Note that you can swap only adjacent digits in the given number.
Examples input
5071 output
4 input
705 output
1 input
1241367 output
-1 Note
In the first example one of the possible sequences of moves is 5071 → 5701 → 7501 → 7510 →7150.