message stringlengths 2 433k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 113 108k | cluster float64 12 12 | __index_level_0__ int64 226 217k |
|---|---|---|---|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Pikachu had an array with him. He wrote down all the non-empty subsequences of the array on paper. Note that an array of size n has 2n - 1 non-empty subsequences in it.
Pikachu being mischievous as he always is, removed all the subsequences in which Maximum_element_of_the_subsequence - Minimum_element_of_subsequence ≥ d
Pikachu was finally left with X subsequences.
However, he lost the initial array he had, and now is in serious trouble. He still remembers the numbers X and d. He now wants you to construct any such array which will satisfy the above conditions. All the numbers in the final array should be positive integers less than 1018.
Note the number of elements in the output array should not be more than 104. If no answer is possible, print - 1.
Input
The only line of input consists of two space separated integers X and d (1 ≤ X, d ≤ 109).
Output
Output should consist of two lines.
First line should contain a single integer n (1 ≤ n ≤ 10 000)— the number of integers in the final array.
Second line should consist of n space separated integers — a1, a2, ... , an (1 ≤ ai < 1018).
If there is no answer, print a single integer -1. If there are multiple answers, print any of them.
Examples
Input
10 5
Output
6
5 50 7 15 6 100
Input
4 2
Output
4
10 100 1000 10000
Note
In the output of the first example case, the remaining subsequences after removing those with Maximum_element_of_the_subsequence - Minimum_element_of_subsequence ≥ 5 are [5], [5, 7], [5, 6], [5, 7, 6], [50], [7], [7, 6], [15], [6], [100]. There are 10 of them. Hence, the array [5, 50, 7, 15, 6, 100] is valid.
Similarly, in the output of the second example case, the remaining sub-sequences after removing those with Maximum_element_of_the_subsequence - Minimum_element_of_subsequence ≥ 2 are [10], [100], [1000], [10000]. There are 4 of them. Hence, the array [10, 100, 1000, 10000] is valid.
Submitted Solution:
```
x,d=map(int,input().split())
c=1
r="\n"
e=29
b=2**e-1
while x:
while x<b:e-=1;b>>=1
r+=f"{c*d} "*e;c+=e;x-=b
print(c-1,r)
``` | instruction | 0 | 106,764 | 12 | 213,528 |
Yes | output | 1 | 106,764 | 12 | 213,529 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Pikachu had an array with him. He wrote down all the non-empty subsequences of the array on paper. Note that an array of size n has 2n - 1 non-empty subsequences in it.
Pikachu being mischievous as he always is, removed all the subsequences in which Maximum_element_of_the_subsequence - Minimum_element_of_subsequence ≥ d
Pikachu was finally left with X subsequences.
However, he lost the initial array he had, and now is in serious trouble. He still remembers the numbers X and d. He now wants you to construct any such array which will satisfy the above conditions. All the numbers in the final array should be positive integers less than 1018.
Note the number of elements in the output array should not be more than 104. If no answer is possible, print - 1.
Input
The only line of input consists of two space separated integers X and d (1 ≤ X, d ≤ 109).
Output
Output should consist of two lines.
First line should contain a single integer n (1 ≤ n ≤ 10 000)— the number of integers in the final array.
Second line should consist of n space separated integers — a1, a2, ... , an (1 ≤ ai < 1018).
If there is no answer, print a single integer -1. If there are multiple answers, print any of them.
Examples
Input
10 5
Output
6
5 50 7 15 6 100
Input
4 2
Output
4
10 100 1000 10000
Note
In the output of the first example case, the remaining subsequences after removing those with Maximum_element_of_the_subsequence - Minimum_element_of_subsequence ≥ 5 are [5], [5, 7], [5, 6], [5, 7, 6], [50], [7], [7, 6], [15], [6], [100]. There are 10 of them. Hence, the array [5, 50, 7, 15, 6, 100] is valid.
Similarly, in the output of the second example case, the remaining sub-sequences after removing those with Maximum_element_of_the_subsequence - Minimum_element_of_subsequence ≥ 2 are [10], [100], [1000], [10000]. There are 4 of them. Hence, the array [10, 100, 1000, 10000] is valid.
Submitted Solution:
```
import math
x,d=map(int,input().split())
n=math.floor(math.log(x+1,2))
if (n-1>=d and x>10000):
print(-1)
elif (x<=10000 or n-1>=d):
print(x)
for i in range(1,x*d+2-d,d):
print(i,end=' ')
print()
else:
tb=2**n-1
diff=x-tb
g=1
arr=[]
c=tb
while diff>0:
for i in range(g,g+n):
arr.append(i)
g=g+n+d-1
n=math.floor(math.log(diff+1,2))
tb=2**n-1
diff=diff-tb
c+=tb
print(c)
print(*arr)
``` | instruction | 0 | 106,765 | 12 | 213,530 |
No | output | 1 | 106,765 | 12 | 213,531 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Pikachu had an array with him. He wrote down all the non-empty subsequences of the array on paper. Note that an array of size n has 2n - 1 non-empty subsequences in it.
Pikachu being mischievous as he always is, removed all the subsequences in which Maximum_element_of_the_subsequence - Minimum_element_of_subsequence ≥ d
Pikachu was finally left with X subsequences.
However, he lost the initial array he had, and now is in serious trouble. He still remembers the numbers X and d. He now wants you to construct any such array which will satisfy the above conditions. All the numbers in the final array should be positive integers less than 1018.
Note the number of elements in the output array should not be more than 104. If no answer is possible, print - 1.
Input
The only line of input consists of two space separated integers X and d (1 ≤ X, d ≤ 109).
Output
Output should consist of two lines.
First line should contain a single integer n (1 ≤ n ≤ 10 000)— the number of integers in the final array.
Second line should consist of n space separated integers — a1, a2, ... , an (1 ≤ ai < 1018).
If there is no answer, print a single integer -1. If there are multiple answers, print any of them.
Examples
Input
10 5
Output
6
5 50 7 15 6 100
Input
4 2
Output
4
10 100 1000 10000
Note
In the output of the first example case, the remaining subsequences after removing those with Maximum_element_of_the_subsequence - Minimum_element_of_subsequence ≥ 5 are [5], [5, 7], [5, 6], [5, 7, 6], [50], [7], [7, 6], [15], [6], [100]. There are 10 of them. Hence, the array [5, 50, 7, 15, 6, 100] is valid.
Similarly, in the output of the second example case, the remaining sub-sequences after removing those with Maximum_element_of_the_subsequence - Minimum_element_of_subsequence ≥ 2 are [10], [100], [1000], [10000]. There are 4 of them. Hence, the array [10, 100, 1000, 10000] is valid.
Submitted Solution:
```
x,d = input().split()
x,d = [int(x),int(d)]
from random import randint
print(2*x)
for i in range(x) :
num = randint(1,100000)
print(num,num-d+1,end = ' ')
``` | instruction | 0 | 106,766 | 12 | 213,532 |
No | output | 1 | 106,766 | 12 | 213,533 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Pikachu had an array with him. He wrote down all the non-empty subsequences of the array on paper. Note that an array of size n has 2n - 1 non-empty subsequences in it.
Pikachu being mischievous as he always is, removed all the subsequences in which Maximum_element_of_the_subsequence - Minimum_element_of_subsequence ≥ d
Pikachu was finally left with X subsequences.
However, he lost the initial array he had, and now is in serious trouble. He still remembers the numbers X and d. He now wants you to construct any such array which will satisfy the above conditions. All the numbers in the final array should be positive integers less than 1018.
Note the number of elements in the output array should not be more than 104. If no answer is possible, print - 1.
Input
The only line of input consists of two space separated integers X and d (1 ≤ X, d ≤ 109).
Output
Output should consist of two lines.
First line should contain a single integer n (1 ≤ n ≤ 10 000)— the number of integers in the final array.
Second line should consist of n space separated integers — a1, a2, ... , an (1 ≤ ai < 1018).
If there is no answer, print a single integer -1. If there are multiple answers, print any of them.
Examples
Input
10 5
Output
6
5 50 7 15 6 100
Input
4 2
Output
4
10 100 1000 10000
Note
In the output of the first example case, the remaining subsequences after removing those with Maximum_element_of_the_subsequence - Minimum_element_of_subsequence ≥ 5 are [5], [5, 7], [5, 6], [5, 7, 6], [50], [7], [7, 6], [15], [6], [100]. There are 10 of them. Hence, the array [5, 50, 7, 15, 6, 100] is valid.
Similarly, in the output of the second example case, the remaining sub-sequences after removing those with Maximum_element_of_the_subsequence - Minimum_element_of_subsequence ≥ 2 are [10], [100], [1000], [10000]. There are 4 of them. Hence, the array [10, 100, 1000, 10000] is valid.
Submitted Solution:
```
n,d=map(int,input().split())
if n==10 and d==5:
n-=1
k=1
s=''
c=0
for i in range(n):
s+=str(k)+' '
k+=d+1
if s=='':
print(-1)
else:
print(n)
print(s[:len(s)-1])
``` | instruction | 0 | 106,767 | 12 | 213,534 |
No | output | 1 | 106,767 | 12 | 213,535 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Pikachu had an array with him. He wrote down all the non-empty subsequences of the array on paper. Note that an array of size n has 2n - 1 non-empty subsequences in it.
Pikachu being mischievous as he always is, removed all the subsequences in which Maximum_element_of_the_subsequence - Minimum_element_of_subsequence ≥ d
Pikachu was finally left with X subsequences.
However, he lost the initial array he had, and now is in serious trouble. He still remembers the numbers X and d. He now wants you to construct any such array which will satisfy the above conditions. All the numbers in the final array should be positive integers less than 1018.
Note the number of elements in the output array should not be more than 104. If no answer is possible, print - 1.
Input
The only line of input consists of two space separated integers X and d (1 ≤ X, d ≤ 109).
Output
Output should consist of two lines.
First line should contain a single integer n (1 ≤ n ≤ 10 000)— the number of integers in the final array.
Second line should consist of n space separated integers — a1, a2, ... , an (1 ≤ ai < 1018).
If there is no answer, print a single integer -1. If there are multiple answers, print any of them.
Examples
Input
10 5
Output
6
5 50 7 15 6 100
Input
4 2
Output
4
10 100 1000 10000
Note
In the output of the first example case, the remaining subsequences after removing those with Maximum_element_of_the_subsequence - Minimum_element_of_subsequence ≥ 5 are [5], [5, 7], [5, 6], [5, 7, 6], [50], [7], [7, 6], [15], [6], [100]. There are 10 of them. Hence, the array [5, 50, 7, 15, 6, 100] is valid.
Similarly, in the output of the second example case, the remaining sub-sequences after removing those with Maximum_element_of_the_subsequence - Minimum_element_of_subsequence ≥ 2 are [10], [100], [1000], [10000]. There are 4 of them. Hence, the array [10, 100, 1000, 10000] is valid.
Submitted Solution:
```
x,d=map(int,input().split())
for i in range (0,x):
print((i+1)*d,end=" ")
``` | instruction | 0 | 106,768 | 12 | 213,536 |
No | output | 1 | 106,768 | 12 | 213,537 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an array a consisting of n integers.
In one move, you can choose two indices 1 ≤ i, j ≤ n such that i ≠ j and set a_i := a_j. You can perform such moves any number of times (possibly, zero). You can choose different indices in different operations. The operation := is the operation of assignment (i.e. you choose i and j and replace a_i with a_j).
Your task is to say if it is possible to obtain an array with an odd (not divisible by 2) sum of elements.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 2000) — the number of test cases.
The next 2t lines describe test cases. The first line of the test case contains one integer n (1 ≤ n ≤ 2000) — the number of elements in a. The second line of the test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 2000), where a_i is the i-th element of a.
It is guaranteed that the sum of n over all test cases does not exceed 2000 (∑ n ≤ 2000).
Output
For each test case, print the answer on it — "YES" (without quotes) if it is possible to obtain the array with an odd sum of elements, and "NO" otherwise.
Example
Input
5
2
2 3
4
2 2 8 8
3
3 3 3
4
5 5 5 5
4
1 1 1 1
Output
YES
NO
YES
NO
NO | instruction | 0 | 107,137 | 12 | 214,274 |
Tags: math
Correct Solution:
```
t = int(input())
for i in range(0,t):
n = int(input())
a = list(map(int,input().split()))
countodd = 0
counteven = 0
for k in range(0,n):
num = a[k]
if(num%2 ==0):
counteven = counteven + 1
else:
countodd = countodd + 1
if(countodd == 0):
print("NO")
else:
if(countodd % 2 == 1):
print('YES')
else:
if(counteven > 0):
print('YES')
else:
print('NO')
``` | output | 1 | 107,137 | 12 | 214,275 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an array a consisting of n integers.
In one move, you can choose two indices 1 ≤ i, j ≤ n such that i ≠ j and set a_i := a_j. You can perform such moves any number of times (possibly, zero). You can choose different indices in different operations. The operation := is the operation of assignment (i.e. you choose i and j and replace a_i with a_j).
Your task is to say if it is possible to obtain an array with an odd (not divisible by 2) sum of elements.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 2000) — the number of test cases.
The next 2t lines describe test cases. The first line of the test case contains one integer n (1 ≤ n ≤ 2000) — the number of elements in a. The second line of the test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 2000), where a_i is the i-th element of a.
It is guaranteed that the sum of n over all test cases does not exceed 2000 (∑ n ≤ 2000).
Output
For each test case, print the answer on it — "YES" (without quotes) if it is possible to obtain the array with an odd sum of elements, and "NO" otherwise.
Example
Input
5
2
2 3
4
2 2 8 8
3
3 3 3
4
5 5 5 5
4
1 1 1 1
Output
YES
NO
YES
NO
NO | instruction | 0 | 107,138 | 12 | 214,276 |
Tags: math
Correct Solution:
```
t = int(input())
for _ in range(t):
n = int(input())
a = list(map(int, input().split()))
p = 0
if n%2:
for i in a:
if i%2:
print('YES')
p += 1
break
else:
k = 0
for i in a:
if not i%2:
k += 1
if k > 0 and k != n:
print('YES')
p += 1
if p == 0:
print('NO')
``` | output | 1 | 107,138 | 12 | 214,277 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an array a consisting of n integers.
In one move, you can choose two indices 1 ≤ i, j ≤ n such that i ≠ j and set a_i := a_j. You can perform such moves any number of times (possibly, zero). You can choose different indices in different operations. The operation := is the operation of assignment (i.e. you choose i and j and replace a_i with a_j).
Your task is to say if it is possible to obtain an array with an odd (not divisible by 2) sum of elements.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 2000) — the number of test cases.
The next 2t lines describe test cases. The first line of the test case contains one integer n (1 ≤ n ≤ 2000) — the number of elements in a. The second line of the test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 2000), where a_i is the i-th element of a.
It is guaranteed that the sum of n over all test cases does not exceed 2000 (∑ n ≤ 2000).
Output
For each test case, print the answer on it — "YES" (without quotes) if it is possible to obtain the array with an odd sum of elements, and "NO" otherwise.
Example
Input
5
2
2 3
4
2 2 8 8
3
3 3 3
4
5 5 5 5
4
1 1 1 1
Output
YES
NO
YES
NO
NO | instruction | 0 | 107,139 | 12 | 214,278 |
Tags: math
Correct Solution:
```
for _ in range(int(input())):
n = int(input())
arr = list(map(int, input().split()))
if sum(arr)%2 != 0:
print("YES")
continue
odd = 0
for i in arr:
if i%2!=0:
odd+=1
if odd == 0: print("NO"); continue
if odd%2==0:
if n-odd > 0:
print("YES")
else:
print("NO")
else:
print("YES")
``` | output | 1 | 107,139 | 12 | 214,279 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an array a consisting of n integers.
In one move, you can choose two indices 1 ≤ i, j ≤ n such that i ≠ j and set a_i := a_j. You can perform such moves any number of times (possibly, zero). You can choose different indices in different operations. The operation := is the operation of assignment (i.e. you choose i and j and replace a_i with a_j).
Your task is to say if it is possible to obtain an array with an odd (not divisible by 2) sum of elements.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 2000) — the number of test cases.
The next 2t lines describe test cases. The first line of the test case contains one integer n (1 ≤ n ≤ 2000) — the number of elements in a. The second line of the test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 2000), where a_i is the i-th element of a.
It is guaranteed that the sum of n over all test cases does not exceed 2000 (∑ n ≤ 2000).
Output
For each test case, print the answer on it — "YES" (without quotes) if it is possible to obtain the array with an odd sum of elements, and "NO" otherwise.
Example
Input
5
2
2 3
4
2 2 8 8
3
3 3 3
4
5 5 5 5
4
1 1 1 1
Output
YES
NO
YES
NO
NO | instruction | 0 | 107,140 | 12 | 214,280 |
Tags: math
Correct Solution:
```
n=int(input())
for i in range(n):
m=int(input())
p=list(map(int,input().split()))
if sum(p)%2!=0:
print("YES")
else:
s=0
f=0
for j in range(len(p)):
if (p[j]%2!=0 ):
s=1
else:
f=1
if s-f==0:
print("YES")
else:
print("NO")
``` | output | 1 | 107,140 | 12 | 214,281 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an array a consisting of n integers.
In one move, you can choose two indices 1 ≤ i, j ≤ n such that i ≠ j and set a_i := a_j. You can perform such moves any number of times (possibly, zero). You can choose different indices in different operations. The operation := is the operation of assignment (i.e. you choose i and j and replace a_i with a_j).
Your task is to say if it is possible to obtain an array with an odd (not divisible by 2) sum of elements.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 2000) — the number of test cases.
The next 2t lines describe test cases. The first line of the test case contains one integer n (1 ≤ n ≤ 2000) — the number of elements in a. The second line of the test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 2000), where a_i is the i-th element of a.
It is guaranteed that the sum of n over all test cases does not exceed 2000 (∑ n ≤ 2000).
Output
For each test case, print the answer on it — "YES" (without quotes) if it is possible to obtain the array with an odd sum of elements, and "NO" otherwise.
Example
Input
5
2
2 3
4
2 2 8 8
3
3 3 3
4
5 5 5 5
4
1 1 1 1
Output
YES
NO
YES
NO
NO | instruction | 0 | 107,141 | 12 | 214,282 |
Tags: math
Correct Solution:
```
for _ in range(int(input())):
n = int(input())
a = list(map(int, input().split()))
f = 0
e = 0
o = 0
for i in range(n):
if a[i]%2==1:
o+=1
else:
e+=1
if o%2==1:
print('YES')
elif e>0 and o>0:
print('YES')
else:
print('NO')
``` | output | 1 | 107,141 | 12 | 214,283 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an array a consisting of n integers.
In one move, you can choose two indices 1 ≤ i, j ≤ n such that i ≠ j and set a_i := a_j. You can perform such moves any number of times (possibly, zero). You can choose different indices in different operations. The operation := is the operation of assignment (i.e. you choose i and j and replace a_i with a_j).
Your task is to say if it is possible to obtain an array with an odd (not divisible by 2) sum of elements.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 2000) — the number of test cases.
The next 2t lines describe test cases. The first line of the test case contains one integer n (1 ≤ n ≤ 2000) — the number of elements in a. The second line of the test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 2000), where a_i is the i-th element of a.
It is guaranteed that the sum of n over all test cases does not exceed 2000 (∑ n ≤ 2000).
Output
For each test case, print the answer on it — "YES" (without quotes) if it is possible to obtain the array with an odd sum of elements, and "NO" otherwise.
Example
Input
5
2
2 3
4
2 2 8 8
3
3 3 3
4
5 5 5 5
4
1 1 1 1
Output
YES
NO
YES
NO
NO | instruction | 0 | 107,142 | 12 | 214,284 |
Tags: math
Correct Solution:
```
t = int(input())
for i in range(t):
n = int(input())
l = input().split()
total = 0
pair = 0
odd = 0
for i in l:
total+=int(i)
if total %2 != 0:
print("YES")
else:
for i in l:
if int(i)%2==0:
pair = 1
else:
odd = 1
if pair!=0 and odd!=0:
print('YES')
break
if odd == 0 or pair == 0:
print('NO')
``` | output | 1 | 107,142 | 12 | 214,285 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an array a consisting of n integers.
In one move, you can choose two indices 1 ≤ i, j ≤ n such that i ≠ j and set a_i := a_j. You can perform such moves any number of times (possibly, zero). You can choose different indices in different operations. The operation := is the operation of assignment (i.e. you choose i and j and replace a_i with a_j).
Your task is to say if it is possible to obtain an array with an odd (not divisible by 2) sum of elements.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 2000) — the number of test cases.
The next 2t lines describe test cases. The first line of the test case contains one integer n (1 ≤ n ≤ 2000) — the number of elements in a. The second line of the test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 2000), where a_i is the i-th element of a.
It is guaranteed that the sum of n over all test cases does not exceed 2000 (∑ n ≤ 2000).
Output
For each test case, print the answer on it — "YES" (without quotes) if it is possible to obtain the array with an odd sum of elements, and "NO" otherwise.
Example
Input
5
2
2 3
4
2 2 8 8
3
3 3 3
4
5 5 5 5
4
1 1 1 1
Output
YES
NO
YES
NO
NO | instruction | 0 | 107,143 | 12 | 214,286 |
Tags: math
Correct Solution:
```
t=int(input())
for i in range(t):
n=int(input())
a=list(map(int,input().split()))
od=0
for i in a:
if i%2==1:
od+=1
if sum(a)%2==1:
print('YES')
else:
if n==od or od==0:
print('NO')
else:
print('YES')
``` | output | 1 | 107,143 | 12 | 214,287 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an array a consisting of n integers.
In one move, you can choose two indices 1 ≤ i, j ≤ n such that i ≠ j and set a_i := a_j. You can perform such moves any number of times (possibly, zero). You can choose different indices in different operations. The operation := is the operation of assignment (i.e. you choose i and j and replace a_i with a_j).
Your task is to say if it is possible to obtain an array with an odd (not divisible by 2) sum of elements.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 2000) — the number of test cases.
The next 2t lines describe test cases. The first line of the test case contains one integer n (1 ≤ n ≤ 2000) — the number of elements in a. The second line of the test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 2000), where a_i is the i-th element of a.
It is guaranteed that the sum of n over all test cases does not exceed 2000 (∑ n ≤ 2000).
Output
For each test case, print the answer on it — "YES" (without quotes) if it is possible to obtain the array with an odd sum of elements, and "NO" otherwise.
Example
Input
5
2
2 3
4
2 2 8 8
3
3 3 3
4
5 5 5 5
4
1 1 1 1
Output
YES
NO
YES
NO
NO | instruction | 0 | 107,144 | 12 | 214,288 |
Tags: math
Correct Solution:
```
def Input():
tem = input().split()
ans = []
for it in tem:
ans.append(int(it))
return ans
from collections import Counter
T = Input()[0]
for tt in range(T):
n = Input()[0]
a = Input()
odd, even, total = 0, 0, 0
for i in range(n):
if a[i]%2==0:
even+=1
else:
odd+=1
total+=a[i]
if total%2==1 or (even>0 and odd>0):
print("YES")
else:
print("NO")
``` | output | 1 | 107,144 | 12 | 214,289 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array a consisting of n integers.
In one move, you can choose two indices 1 ≤ i, j ≤ n such that i ≠ j and set a_i := a_j. You can perform such moves any number of times (possibly, zero). You can choose different indices in different operations. The operation := is the operation of assignment (i.e. you choose i and j and replace a_i with a_j).
Your task is to say if it is possible to obtain an array with an odd (not divisible by 2) sum of elements.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 2000) — the number of test cases.
The next 2t lines describe test cases. The first line of the test case contains one integer n (1 ≤ n ≤ 2000) — the number of elements in a. The second line of the test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 2000), where a_i is the i-th element of a.
It is guaranteed that the sum of n over all test cases does not exceed 2000 (∑ n ≤ 2000).
Output
For each test case, print the answer on it — "YES" (without quotes) if it is possible to obtain the array with an odd sum of elements, and "NO" otherwise.
Example
Input
5
2
2 3
4
2 2 8 8
3
3 3 3
4
5 5 5 5
4
1 1 1 1
Output
YES
NO
YES
NO
NO
Submitted Solution:
```
t = int(input())
for _ in range(t):
n = int(input())
a = list(map(int, input().split()))
odds = [a[i] % 2 == 1 for i in range(n)]
evens = [a[i] % 2 == 0 for i in range(n)]
if sum(a) % 2 == 0 and (all(odds) or all(evens)):
print('NO')
else:
print('YES')
``` | instruction | 0 | 107,145 | 12 | 214,290 |
Yes | output | 1 | 107,145 | 12 | 214,291 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array a consisting of n integers.
In one move, you can choose two indices 1 ≤ i, j ≤ n such that i ≠ j and set a_i := a_j. You can perform such moves any number of times (possibly, zero). You can choose different indices in different operations. The operation := is the operation of assignment (i.e. you choose i and j and replace a_i with a_j).
Your task is to say if it is possible to obtain an array with an odd (not divisible by 2) sum of elements.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 2000) — the number of test cases.
The next 2t lines describe test cases. The first line of the test case contains one integer n (1 ≤ n ≤ 2000) — the number of elements in a. The second line of the test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 2000), where a_i is the i-th element of a.
It is guaranteed that the sum of n over all test cases does not exceed 2000 (∑ n ≤ 2000).
Output
For each test case, print the answer on it — "YES" (without quotes) if it is possible to obtain the array with an odd sum of elements, and "NO" otherwise.
Example
Input
5
2
2 3
4
2 2 8 8
3
3 3 3
4
5 5 5 5
4
1 1 1 1
Output
YES
NO
YES
NO
NO
Submitted Solution:
```
for _ in range (int(input())):
n=int(input())
x=[int(n) for n in input().split()]
od=0
for i in x:
if i&1:
od+=1
ev=n-od
if (od&1 or (od%2==0 and ev>0)) and od!=0:
print("YES")
else:
print("NO")
``` | instruction | 0 | 107,146 | 12 | 214,292 |
Yes | output | 1 | 107,146 | 12 | 214,293 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array a consisting of n integers.
In one move, you can choose two indices 1 ≤ i, j ≤ n such that i ≠ j and set a_i := a_j. You can perform such moves any number of times (possibly, zero). You can choose different indices in different operations. The operation := is the operation of assignment (i.e. you choose i and j and replace a_i with a_j).
Your task is to say if it is possible to obtain an array with an odd (not divisible by 2) sum of elements.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 2000) — the number of test cases.
The next 2t lines describe test cases. The first line of the test case contains one integer n (1 ≤ n ≤ 2000) — the number of elements in a. The second line of the test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 2000), where a_i is the i-th element of a.
It is guaranteed that the sum of n over all test cases does not exceed 2000 (∑ n ≤ 2000).
Output
For each test case, print the answer on it — "YES" (without quotes) if it is possible to obtain the array with an odd sum of elements, and "NO" otherwise.
Example
Input
5
2
2 3
4
2 2 8 8
3
3 3 3
4
5 5 5 5
4
1 1 1 1
Output
YES
NO
YES
NO
NO
Submitted Solution:
```
for _ in range(int(input())):
n=int(input())
l = list(map(int,input().split()))
count_odd = 0
for i in range(n):
if(l[i]%2==1):
count_odd+=1
if(count_odd==n)and(n%2==0):
print("NO")
else:
if(count_odd==0):
print("NO")
else:
print("YES")
``` | instruction | 0 | 107,147 | 12 | 214,294 |
Yes | output | 1 | 107,147 | 12 | 214,295 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array a consisting of n integers.
In one move, you can choose two indices 1 ≤ i, j ≤ n such that i ≠ j and set a_i := a_j. You can perform such moves any number of times (possibly, zero). You can choose different indices in different operations. The operation := is the operation of assignment (i.e. you choose i and j and replace a_i with a_j).
Your task is to say if it is possible to obtain an array with an odd (not divisible by 2) sum of elements.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 2000) — the number of test cases.
The next 2t lines describe test cases. The first line of the test case contains one integer n (1 ≤ n ≤ 2000) — the number of elements in a. The second line of the test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 2000), where a_i is the i-th element of a.
It is guaranteed that the sum of n over all test cases does not exceed 2000 (∑ n ≤ 2000).
Output
For each test case, print the answer on it — "YES" (without quotes) if it is possible to obtain the array with an odd sum of elements, and "NO" otherwise.
Example
Input
5
2
2 3
4
2 2 8 8
3
3 3 3
4
5 5 5 5
4
1 1 1 1
Output
YES
NO
YES
NO
NO
Submitted Solution:
```
# You
# Dont read my code
n = int(input())
i = 0
ans = []
while i < n:
x = int(input())
aa = len([ i for i in map(int,input().split()) if i % 2 != 0])
if (aa == 0 or aa % 2 == 0):
if aa == x or aa == 0:
ans.append("NO")
else:
ans.append("YES")
else:
ans.append("YES")
i += 1
for i in ans:
print(i)
``` | instruction | 0 | 107,148 | 12 | 214,296 |
Yes | output | 1 | 107,148 | 12 | 214,297 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array a consisting of n integers.
In one move, you can choose two indices 1 ≤ i, j ≤ n such that i ≠ j and set a_i := a_j. You can perform such moves any number of times (possibly, zero). You can choose different indices in different operations. The operation := is the operation of assignment (i.e. you choose i and j and replace a_i with a_j).
Your task is to say if it is possible to obtain an array with an odd (not divisible by 2) sum of elements.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 2000) — the number of test cases.
The next 2t lines describe test cases. The first line of the test case contains one integer n (1 ≤ n ≤ 2000) — the number of elements in a. The second line of the test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 2000), where a_i is the i-th element of a.
It is guaranteed that the sum of n over all test cases does not exceed 2000 (∑ n ≤ 2000).
Output
For each test case, print the answer on it — "YES" (without quotes) if it is possible to obtain the array with an odd sum of elements, and "NO" otherwise.
Example
Input
5
2
2 3
4
2 2 8 8
3
3 3 3
4
5 5 5 5
4
1 1 1 1
Output
YES
NO
YES
NO
NO
Submitted Solution:
```
def fun(ls):
if(sum(ls)%2==0):
print('NO')
else:
print('YES')
T = int(input())
for i in range(T):
# var=input()
val=int(input())
# st=input()
# ms= list(map(int, input().split()))
ls= list(map(int, input().split()))
# fun(ls)
# v=(int(input()))
fun(ls)
``` | instruction | 0 | 107,149 | 12 | 214,298 |
No | output | 1 | 107,149 | 12 | 214,299 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array a consisting of n integers.
In one move, you can choose two indices 1 ≤ i, j ≤ n such that i ≠ j and set a_i := a_j. You can perform such moves any number of times (possibly, zero). You can choose different indices in different operations. The operation := is the operation of assignment (i.e. you choose i and j and replace a_i with a_j).
Your task is to say if it is possible to obtain an array with an odd (not divisible by 2) sum of elements.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 2000) — the number of test cases.
The next 2t lines describe test cases. The first line of the test case contains one integer n (1 ≤ n ≤ 2000) — the number of elements in a. The second line of the test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 2000), where a_i is the i-th element of a.
It is guaranteed that the sum of n over all test cases does not exceed 2000 (∑ n ≤ 2000).
Output
For each test case, print the answer on it — "YES" (without quotes) if it is possible to obtain the array with an odd sum of elements, and "NO" otherwise.
Example
Input
5
2
2 3
4
2 2 8 8
3
3 3 3
4
5 5 5 5
4
1 1 1 1
Output
YES
NO
YES
NO
NO
Submitted Solution:
```
t=int(input())
for i in range(t):
n=int(input())
a=list(map(int,input().split()))
if sum(a)%2!=0:
print("YES")
else:
ec=0
oc=0
for i in range(len(a)):
if a[i]%2==0:
ec+=a[i]
else:
oc+=a[i]
if ec==oc:
print("NO")
else:
print("YES")
``` | instruction | 0 | 107,150 | 12 | 214,300 |
No | output | 1 | 107,150 | 12 | 214,301 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array a consisting of n integers.
In one move, you can choose two indices 1 ≤ i, j ≤ n such that i ≠ j and set a_i := a_j. You can perform such moves any number of times (possibly, zero). You can choose different indices in different operations. The operation := is the operation of assignment (i.e. you choose i and j and replace a_i with a_j).
Your task is to say if it is possible to obtain an array with an odd (not divisible by 2) sum of elements.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 2000) — the number of test cases.
The next 2t lines describe test cases. The first line of the test case contains one integer n (1 ≤ n ≤ 2000) — the number of elements in a. The second line of the test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 2000), where a_i is the i-th element of a.
It is guaranteed that the sum of n over all test cases does not exceed 2000 (∑ n ≤ 2000).
Output
For each test case, print the answer on it — "YES" (without quotes) if it is possible to obtain the array with an odd sum of elements, and "NO" otherwise.
Example
Input
5
2
2 3
4
2 2 8 8
3
3 3 3
4
5 5 5 5
4
1 1 1 1
Output
YES
NO
YES
NO
NO
Submitted Solution:
```
for _ in range(int(input())):
n = int(input())
a = list(map(int, input().split()))
if sum(a) % 2 == 0:
print('NO')
else:
print('YES')
``` | instruction | 0 | 107,151 | 12 | 214,302 |
No | output | 1 | 107,151 | 12 | 214,303 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array a consisting of n integers.
In one move, you can choose two indices 1 ≤ i, j ≤ n such that i ≠ j and set a_i := a_j. You can perform such moves any number of times (possibly, zero). You can choose different indices in different operations. The operation := is the operation of assignment (i.e. you choose i and j and replace a_i with a_j).
Your task is to say if it is possible to obtain an array with an odd (not divisible by 2) sum of elements.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 2000) — the number of test cases.
The next 2t lines describe test cases. The first line of the test case contains one integer n (1 ≤ n ≤ 2000) — the number of elements in a. The second line of the test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 2000), where a_i is the i-th element of a.
It is guaranteed that the sum of n over all test cases does not exceed 2000 (∑ n ≤ 2000).
Output
For each test case, print the answer on it — "YES" (without quotes) if it is possible to obtain the array with an odd sum of elements, and "NO" otherwise.
Example
Input
5
2
2 3
4
2 2 8 8
3
3 3 3
4
5 5 5 5
4
1 1 1 1
Output
YES
NO
YES
NO
NO
Submitted Solution:
```
n=int(input())
for i in range(n):
m=int(input())
p=list(map(int,input().split()))
if sum(p)%2!=0:
print("YES")
else:
print("NO")
``` | instruction | 0 | 107,152 | 12 | 214,304 |
No | output | 1 | 107,152 | 12 | 214,305 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Consider the infinite sequence s of positive integers, created by repeating the following steps:
1. Find the lexicographically smallest triple of positive integers (a, b, c) such that
* a ⊕ b ⊕ c = 0, where ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).
* a, b, c are not in s.
Here triple of integers (a_1, b_1, c_1) is considered to be lexicographically smaller than triple (a_2, b_2, c_2) if sequence [a_1, b_1, c_1] is lexicographically smaller than sequence [a_2, b_2, c_2].
2. Append a, b, c to s in this order.
3. Go back to the first step.
You have integer n. Find the n-th element of s.
You have to answer t independent test cases.
A sequence a is lexicographically smaller than a sequence b if in the first position where a and b differ, the sequence a has a smaller element than the corresponding element in b.
Input
The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases.
Each of the next t lines contains a single integer n (1≤ n ≤ 10^{16}) — the position of the element you want to know.
Output
In each of the t lines, output the answer to the corresponding test case.
Example
Input
9
1
2
3
4
5
6
7
8
9
Output
1
2
3
4
8
12
5
10
15
Note
The first elements of s are 1, 2, 3, 4, 8, 12, 5, 10, 15, ... | instruction | 0 | 107,169 | 12 | 214,338 |
Tags: bitmasks, brute force, constructive algorithms, divide and conquer, math
Correct Solution:
```
from collections import defaultdict
from queue import deque
from sys import stdin, stdout
from math import log2
def arrinp():
return [*map(int, stdin.readline().split(' '))]
def mulinp():
return map(int, stdin.readline().split(' '))
def intinp():
return int(stdin.readline())
def solution():
n = intinp()
if n <= 3:
print(n)
return
if n % 3 == 1:
k = n.bit_length()-1
if k & 1:
k -= 1
print(2**k + (n-2**k) // 3)
elif n % 3 == 2:
n1 = n-1
k = n1.bit_length()-1
if k & 1:
k -= 1
ans1 = 2**k + (n1-2**k) // 3
ans = 0
cnt = 0
while ans1:
a = ans1 % 4
if a == 1:
a = 2
elif a == 2:
a = 3
elif a == 3:
a = 1
ans += a * (4**cnt)
cnt += 1
ans1 >>= 2
print(ans)
else:
n1 = n - 2
k = n1.bit_length()-1
if k & 1:
k -= 1
ans1 = 2 ** k + (n1 - 2 ** k) // 3
ans = 0
cnt = 0
while ans1:
a = ans1 % 4
if a == 1:
a = 3
elif a == 2:
a = 1
elif a == 3:
a = 2
ans += a * (4 ** cnt)
cnt += 1
ans1 >>= 2
print(ans)
testcases = 1
testcases = intinp()
for _ in range(testcases):
solution()
``` | output | 1 | 107,169 | 12 | 214,339 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Consider the infinite sequence s of positive integers, created by repeating the following steps:
1. Find the lexicographically smallest triple of positive integers (a, b, c) such that
* a ⊕ b ⊕ c = 0, where ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).
* a, b, c are not in s.
Here triple of integers (a_1, b_1, c_1) is considered to be lexicographically smaller than triple (a_2, b_2, c_2) if sequence [a_1, b_1, c_1] is lexicographically smaller than sequence [a_2, b_2, c_2].
2. Append a, b, c to s in this order.
3. Go back to the first step.
You have integer n. Find the n-th element of s.
You have to answer t independent test cases.
A sequence a is lexicographically smaller than a sequence b if in the first position where a and b differ, the sequence a has a smaller element than the corresponding element in b.
Input
The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases.
Each of the next t lines contains a single integer n (1≤ n ≤ 10^{16}) — the position of the element you want to know.
Output
In each of the t lines, output the answer to the corresponding test case.
Example
Input
9
1
2
3
4
5
6
7
8
9
Output
1
2
3
4
8
12
5
10
15
Note
The first elements of s are 1, 2, 3, 4, 8, 12, 5, 10, 15, ... | instruction | 0 | 107,170 | 12 | 214,340 |
Tags: bitmasks, brute force, constructive algorithms, divide and conquer, math
Correct Solution:
```
import sys
input = sys.stdin.readline
t = int(input())
s = [int(input()) for i in range(t)]
res = []
for num in s:
num -= 1
mod = num % 3
num = num // 3
div = 1
while True:
if num // div != 0:
num -= div
div *= 4
else:
break
a = div + num
b = a * 2
tmp = a
coff = 1
while True:
if tmp == 0:
break
if tmp % 4 == 2:
b -= coff
if tmp % 4 == 3:
b -= coff * 5
tmp = tmp // 4
coff *= 4
c = a ^ b
if mod == 0:
print(a)
if mod == 1:
print(b)
if mod == 2:
print(c)
``` | output | 1 | 107,170 | 12 | 214,341 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Consider the infinite sequence s of positive integers, created by repeating the following steps:
1. Find the lexicographically smallest triple of positive integers (a, b, c) such that
* a ⊕ b ⊕ c = 0, where ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).
* a, b, c are not in s.
Here triple of integers (a_1, b_1, c_1) is considered to be lexicographically smaller than triple (a_2, b_2, c_2) if sequence [a_1, b_1, c_1] is lexicographically smaller than sequence [a_2, b_2, c_2].
2. Append a, b, c to s in this order.
3. Go back to the first step.
You have integer n. Find the n-th element of s.
You have to answer t independent test cases.
A sequence a is lexicographically smaller than a sequence b if in the first position where a and b differ, the sequence a has a smaller element than the corresponding element in b.
Input
The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases.
Each of the next t lines contains a single integer n (1≤ n ≤ 10^{16}) — the position of the element you want to know.
Output
In each of the t lines, output the answer to the corresponding test case.
Example
Input
9
1
2
3
4
5
6
7
8
9
Output
1
2
3
4
8
12
5
10
15
Note
The first elements of s are 1, 2, 3, 4, 8, 12, 5, 10, 15, ... | instruction | 0 | 107,171 | 12 | 214,342 |
Tags: bitmasks, brute force, constructive algorithms, divide and conquer, math
Correct Solution:
```
#!/usr/bin/env python3
import sys
input = sys.stdin.readline
from itertools import combinations
t = int(input())
for tt in range(t):
n = int(input()) - 1
mod3 = n % 3
n = n // 3
i = 0
while n >= 4**i:
n -= 4**i
i += 1
if i == 0:
a = 1; b = 2; c = 3
else:
a = 4**i + n
left = 0
right = 4**i
b = 4**i * 2
t = n
while right - left > 1:
mid1 = (left * 3 + right) // 4
mid2 = (left * 2 + right * 2) // 4
mid3 = (left + right * 3) // 4
rng = right - left
if left <= t < mid1:
b += 0
elif mid1 <= t < mid2:
b += rng // 4 * 2
elif mid2 <= t < mid3:
b += rng // 4 * 3
else:
b += rng // 4 * 1
t %= rng // 4
right //= 4
c = a ^ b
# print("#", tt + 1)
if mod3 == 0:
print(a)
elif mod3 == 1:
print(b)
else:
print(c)
# not_used = set([item for item in range(1, 200)])
# for i in range(25):
# li = list(not_used)
# li.sort()
# for comb in combinations(li, 3):
# if comb[0] ^ comb[1] ^ comb[2] == 0:
# print(comb)
# not_used.remove(comb[0])
# not_used.remove(comb[1])
# not_used.remove(comb[2])
# break
``` | output | 1 | 107,171 | 12 | 214,343 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Consider the infinite sequence s of positive integers, created by repeating the following steps:
1. Find the lexicographically smallest triple of positive integers (a, b, c) such that
* a ⊕ b ⊕ c = 0, where ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).
* a, b, c are not in s.
Here triple of integers (a_1, b_1, c_1) is considered to be lexicographically smaller than triple (a_2, b_2, c_2) if sequence [a_1, b_1, c_1] is lexicographically smaller than sequence [a_2, b_2, c_2].
2. Append a, b, c to s in this order.
3. Go back to the first step.
You have integer n. Find the n-th element of s.
You have to answer t independent test cases.
A sequence a is lexicographically smaller than a sequence b if in the first position where a and b differ, the sequence a has a smaller element than the corresponding element in b.
Input
The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases.
Each of the next t lines contains a single integer n (1≤ n ≤ 10^{16}) — the position of the element you want to know.
Output
In each of the t lines, output the answer to the corresponding test case.
Example
Input
9
1
2
3
4
5
6
7
8
9
Output
1
2
3
4
8
12
5
10
15
Note
The first elements of s are 1, 2, 3, 4, 8, 12, 5, 10, 15, ... | instruction | 0 | 107,172 | 12 | 214,344 |
Tags: bitmasks, brute force, constructive algorithms, divide and conquer, math
Correct Solution:
```
# ------------------- fast io --------------------
import os
import sys
from io import BytesIO, IOBase
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
# ------------------- fast io --------------------
from math import gcd, ceil
def prod(a, mod=10**9+7):
ans = 1
for each in a:
ans = (ans * each) % mod
return ans
def lcm(a, b): return a * b // gcd(a, b)
def binary(x, length=16):
y = bin(x)[2:]
return y if len(y) >= length else "0" * (length - len(y)) + y
for _ in range(int(input()) if True else 1):
n = int(input())
# if n % 3 == 1:
# 1, 4-7, 16-31, 64-127, 256-511
def f1(x, pow=1):
if x > 4**pow:
return f1(x-4**pow, pow+1)
return 4**pow + (x - 1)
# if n % 3 == 2:
# 2, (8,10,11,9), (32->35,40->43,44->47,36->39)
# follow 1, 3, 4, 2 pattern
def f2(x, pow=1):
if x > 4**pow:
return f2(x-4**pow, pow+1)
alpha = 2*(4**pow)
# x is between 1 and 4^pow
while x > 4:
rem = (x-1) // (4**(pow-1))
alpha += 4**(pow-1)*[0, 2, 3, 1][rem]
x -= 4**(pow-1) * rem
pow -= 1
return alpha + [0,2,3,1][x-1]
# if n % 3 == 0:
# use previous two numbers to calculate
if n <= 3:
print(n)
continue
if n % 3 == 1:
n //= 3
print(f1(n))
elif n % 3 == 2:
n //= 3
print(f2(n))
elif n % 3 == 0:
n //= 3
n -= 1
print(f1(n)^f2(n))
``` | output | 1 | 107,172 | 12 | 214,345 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Consider the infinite sequence s of positive integers, created by repeating the following steps:
1. Find the lexicographically smallest triple of positive integers (a, b, c) such that
* a ⊕ b ⊕ c = 0, where ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).
* a, b, c are not in s.
Here triple of integers (a_1, b_1, c_1) is considered to be lexicographically smaller than triple (a_2, b_2, c_2) if sequence [a_1, b_1, c_1] is lexicographically smaller than sequence [a_2, b_2, c_2].
2. Append a, b, c to s in this order.
3. Go back to the first step.
You have integer n. Find the n-th element of s.
You have to answer t independent test cases.
A sequence a is lexicographically smaller than a sequence b if in the first position where a and b differ, the sequence a has a smaller element than the corresponding element in b.
Input
The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases.
Each of the next t lines contains a single integer n (1≤ n ≤ 10^{16}) — the position of the element you want to know.
Output
In each of the t lines, output the answer to the corresponding test case.
Example
Input
9
1
2
3
4
5
6
7
8
9
Output
1
2
3
4
8
12
5
10
15
Note
The first elements of s are 1, 2, 3, 4, 8, 12, 5, 10, 15, ... | instruction | 0 | 107,173 | 12 | 214,346 |
Tags: bitmasks, brute force, constructive algorithms, divide and conquer, math
Correct Solution:
```
import os
import sys
input = sys.stdin.buffer.readline
#sys.setrecursionlimit(int(3e5))
from collections import deque
from queue import PriorityQueue
import math
# list(map(int, input().split()))
#####################################################################################
class CF(object):
def __init__(self):
self.g = []
for i in range(100):
self.g.append( (4**i) * 3)
def gao(self, x, n):
#print(str(x) + ' '+ str(n))
re = deque()
rest = x%3
cnt = int(x//3)
for i in range(n):
re.appendleft(cnt%4)
cnt = int(cnt//4)
pass
ans = (rest+1)
for i in range(n):
ans<<=2
if(re[i]== 1):
ans+=rest+1
elif(re[i]==2):
if(rest == 0):
ans+=2
elif(rest == 1):
ans+=3
elif(rest == 2):
ans+=1
elif(re[i]==3):
if(rest == 0):
ans+=3
elif(rest==1):
ans+=1
elif(rest == 2):
ans+=2
pass
print(ans)
def main(self):
self.t = int(input())
for _ in range(self.t):
pos = int(input())
now = 0
while(True):
if(pos>self.g[now]):
pos-=self.g[now]
now+=1
else:
break
pass
x = pos-1
self.gao(x, now)
pass
if __name__ == "__main__":
cf = CF()
cf.main()
pass
``` | output | 1 | 107,173 | 12 | 214,347 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Consider the infinite sequence s of positive integers, created by repeating the following steps:
1. Find the lexicographically smallest triple of positive integers (a, b, c) such that
* a ⊕ b ⊕ c = 0, where ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).
* a, b, c are not in s.
Here triple of integers (a_1, b_1, c_1) is considered to be lexicographically smaller than triple (a_2, b_2, c_2) if sequence [a_1, b_1, c_1] is lexicographically smaller than sequence [a_2, b_2, c_2].
2. Append a, b, c to s in this order.
3. Go back to the first step.
You have integer n. Find the n-th element of s.
You have to answer t independent test cases.
A sequence a is lexicographically smaller than a sequence b if in the first position where a and b differ, the sequence a has a smaller element than the corresponding element in b.
Input
The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases.
Each of the next t lines contains a single integer n (1≤ n ≤ 10^{16}) — the position of the element you want to know.
Output
In each of the t lines, output the answer to the corresponding test case.
Example
Input
9
1
2
3
4
5
6
7
8
9
Output
1
2
3
4
8
12
5
10
15
Note
The first elements of s are 1, 2, 3, 4, 8, 12, 5, 10, 15, ... | instruction | 0 | 107,174 | 12 | 214,348 |
Tags: bitmasks, brute force, constructive algorithms, divide and conquer, math
Correct Solution:
```
mod = 1000000007
eps = 10**-9
def main():
import sys
input = sys.stdin.buffer.readline
for _ in range(int(input())):
N = int(input())
if N <= 3:
print(N)
continue
if N%3 == 1:
k = N.bit_length()-1
if k&1:
k -= 1
print(2**k + (N-2**k) // 3)
elif N%3 == 2:
N1 = N-1
k = N1.bit_length()-1
if k&1:
k -= 1
ans1 = 2**k + (N1-2**k) // 3
ans = 0
cnt = 0
while ans1:
a = ans1 % 4
if a == 1:
a = 2
elif a == 2:
a = 3
elif a == 3:
a = 1
ans += a * (4**cnt)
cnt += 1
ans1 >>= 2
print(ans)
else:
N1 = N - 2
k = N1.bit_length()-1
if k & 1:
k -= 1
ans1 = 2 ** k + (N1 - 2 ** k) // 3
ans = 0
cnt = 0
while ans1:
a = ans1 % 4
if a == 1:
a = 3
elif a == 2:
a = 1
elif a == 3:
a = 2
ans += a * (4 ** cnt)
cnt += 1
ans1 >>= 2
print(ans)
if __name__ == '__main__':
main()
``` | output | 1 | 107,174 | 12 | 214,349 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Consider the infinite sequence s of positive integers, created by repeating the following steps:
1. Find the lexicographically smallest triple of positive integers (a, b, c) such that
* a ⊕ b ⊕ c = 0, where ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).
* a, b, c are not in s.
Here triple of integers (a_1, b_1, c_1) is considered to be lexicographically smaller than triple (a_2, b_2, c_2) if sequence [a_1, b_1, c_1] is lexicographically smaller than sequence [a_2, b_2, c_2].
2. Append a, b, c to s in this order.
3. Go back to the first step.
You have integer n. Find the n-th element of s.
You have to answer t independent test cases.
A sequence a is lexicographically smaller than a sequence b if in the first position where a and b differ, the sequence a has a smaller element than the corresponding element in b.
Input
The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases.
Each of the next t lines contains a single integer n (1≤ n ≤ 10^{16}) — the position of the element you want to know.
Output
In each of the t lines, output the answer to the corresponding test case.
Example
Input
9
1
2
3
4
5
6
7
8
9
Output
1
2
3
4
8
12
5
10
15
Note
The first elements of s are 1, 2, 3, 4, 8, 12, 5, 10, 15, ... | instruction | 0 | 107,175 | 12 | 214,350 |
Tags: bitmasks, brute force, constructive algorithms, divide and conquer, math
Correct Solution:
```
import sys
input = sys.stdin.readline
out = []
t = int(input())
for _ in range(t):
n = int(input())
n -= 1
rem = n % 3
n //= 3
s = []
if n:
n -= 1
while n >= 0:
s.append([['00','00','00'],['01','10','11'],['10','11','01'],['11','01','10']][n % 4][rem])
n //= 4
n -= 1
s.append(['1','10','11'][rem])
s.reverse()
out.append(int(''.join(s),2))
print('\n'.join(map(str,out)))
``` | output | 1 | 107,175 | 12 | 214,351 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Consider the infinite sequence s of positive integers, created by repeating the following steps:
1. Find the lexicographically smallest triple of positive integers (a, b, c) such that
* a ⊕ b ⊕ c = 0, where ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).
* a, b, c are not in s.
Here triple of integers (a_1, b_1, c_1) is considered to be lexicographically smaller than triple (a_2, b_2, c_2) if sequence [a_1, b_1, c_1] is lexicographically smaller than sequence [a_2, b_2, c_2].
2. Append a, b, c to s in this order.
3. Go back to the first step.
You have integer n. Find the n-th element of s.
You have to answer t independent test cases.
A sequence a is lexicographically smaller than a sequence b if in the first position where a and b differ, the sequence a has a smaller element than the corresponding element in b.
Input
The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases.
Each of the next t lines contains a single integer n (1≤ n ≤ 10^{16}) — the position of the element you want to know.
Output
In each of the t lines, output the answer to the corresponding test case.
Example
Input
9
1
2
3
4
5
6
7
8
9
Output
1
2
3
4
8
12
5
10
15
Note
The first elements of s are 1, 2, 3, 4, 8, 12, 5, 10, 15, ... | instruction | 0 | 107,176 | 12 | 214,352 |
Tags: bitmasks, brute force, constructive algorithms, divide and conquer, math
Correct Solution:
```
import os
import sys
mapper = {"00": "00", "01": "10", "10": "11", "11": "01"}
def f(n):
n1 = (n - 1) // 3
if n1 >= 1466015503701:
x = 1466015503701
i = 21
else:
x = 0
i = 0
while n1 >= x + 4 ** i:
x += 4 ** i
i += 1
t1 = 4 ** i + n1 - x
t2 = int(
"10" + "".join(mapper[bin(t1)[3:][2 * j : 2 * (j + 1)]] for j in range(i)), 2
)
idx = n - n1 * 3 - 1
if idx == 0:
return t1
elif idx == 1:
return t2
elif idx == 2:
return t1 ^ t2
else:
raise Exception("bug")
def pp(input):
T = int(input())
print("\n".join(map(str, (f(int(input())) for _ in range(T)))))
if "paalto" in os.getcwd() and "pydevconsole" in sys.argv[0]:
from string_source import string_source
pp(
string_source(
"""9
1
2
3
4
5
6
7
8
9"""
)
)
else:
input = sys.stdin.buffer.readline
pp(input)
assert f(999999999990000) == 1046445486432677
def x():
for i in range(100000):
f(999999999990000 + i)
# %timeit -n 1 x()
``` | output | 1 | 107,176 | 12 | 214,353 |
Provide a correct Python 3 solution for this coding contest problem.
For $n$ dynamic arrays $A_i$ ($i = 0, 1, ..., n-1$), perform a sequence of the following operations:
* pushBack($t$, $x$): Add element $x$ at the end of $A_t$.
* dump($t$): Print all elements in $A_t$.
* clear($t$): Clear $A_t$. If $A_t$ is empty, do nothing.
$A_i$ is a 0-origin array and it is empty in the initial state.
Constraints
* $1 \leq n \leq 1,000$
* $1 \leq q \leq 500,000$
* $-1,000,000,000 \leq x \leq 1,000,000,000$
* The total number of elements printed by dump operations do not exceed 500,000
Input
The input is given in the following format.
$n$ $q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $t$ $x$
or
1 $t$
or
2 $t$
where the first digits 0, 1 and 2 represent pushBack, dump and clear operations respectively.
Output
For each dump operation, print elements of $A_t$ a line. Separete adjacency elements by a space character (do not print the space after the last element). Note that, if the array is empty, an empty line should be printed.
Example
Input
3 13
0 0 1
0 0 2
0 0 3
0 1 -1
0 2 4
0 2 5
1 0
1 1
1 2
2 1
1 0
1 1
1 2
Output
1 2 3
-1
4 5
1 2 3
4 5 | instruction | 0 | 107,846 | 12 | 215,692 |
"Correct Solution:
```
from collections import deque
if __name__ == '__main__':
n, q = input().split()
n, q= int(n), int(q)
lists = [deque([]) for i in range(n)]
for i in range(q):
p = input().split()
if p[0] == '0':
lists[int(p[1])].append(p[2])
elif p[0] == '1':
frag = False
for i in lists[int(p[1])]:
print(' ' + i if frag else i, end = '')
frag = True
print()
else:
lists[int(p[1])].clear()
``` | output | 1 | 107,846 | 12 | 215,693 |
Provide a correct Python 3 solution for this coding contest problem.
For $n$ dynamic arrays $A_i$ ($i = 0, 1, ..., n-1$), perform a sequence of the following operations:
* pushBack($t$, $x$): Add element $x$ at the end of $A_t$.
* dump($t$): Print all elements in $A_t$.
* clear($t$): Clear $A_t$. If $A_t$ is empty, do nothing.
$A_i$ is a 0-origin array and it is empty in the initial state.
Constraints
* $1 \leq n \leq 1,000$
* $1 \leq q \leq 500,000$
* $-1,000,000,000 \leq x \leq 1,000,000,000$
* The total number of elements printed by dump operations do not exceed 500,000
Input
The input is given in the following format.
$n$ $q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $t$ $x$
or
1 $t$
or
2 $t$
where the first digits 0, 1 and 2 represent pushBack, dump and clear operations respectively.
Output
For each dump operation, print elements of $A_t$ a line. Separete adjacency elements by a space character (do not print the space after the last element). Note that, if the array is empty, an empty line should be printed.
Example
Input
3 13
0 0 1
0 0 2
0 0 3
0 1 -1
0 2 4
0 2 5
1 0
1 1
1 2
2 1
1 0
1 1
1 2
Output
1 2 3
-1
4 5
1 2 3
4 5 | instruction | 0 | 107,849 | 12 | 215,698 |
"Correct Solution:
```
import sys
n, q = map(int, input().split())
A = [[] for _ in range(n)]
for _ in range(q):
query = list(map(int,sys.stdin.readline().split()))
# query = list(map(int, input().split()))
if query[0] == 0:
A[query[1]].append(query[2])
elif query[0] == 1:
print(*A[query[1]])
else:
del A[query[1]][:]
``` | output | 1 | 107,849 | 12 | 215,699 |
Provide a correct Python 3 solution for this coding contest problem.
For $n$ dynamic arrays $A_i$ ($i = 0, 1, ..., n-1$), perform a sequence of the following operations:
* pushBack($t$, $x$): Add element $x$ at the end of $A_t$.
* dump($t$): Print all elements in $A_t$.
* clear($t$): Clear $A_t$. If $A_t$ is empty, do nothing.
$A_i$ is a 0-origin array and it is empty in the initial state.
Constraints
* $1 \leq n \leq 1,000$
* $1 \leq q \leq 500,000$
* $-1,000,000,000 \leq x \leq 1,000,000,000$
* The total number of elements printed by dump operations do not exceed 500,000
Input
The input is given in the following format.
$n$ $q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $t$ $x$
or
1 $t$
or
2 $t$
where the first digits 0, 1 and 2 represent pushBack, dump and clear operations respectively.
Output
For each dump operation, print elements of $A_t$ a line. Separete adjacency elements by a space character (do not print the space after the last element). Note that, if the array is empty, an empty line should be printed.
Example
Input
3 13
0 0 1
0 0 2
0 0 3
0 1 -1
0 2 4
0 2 5
1 0
1 1
1 2
2 1
1 0
1 1
1 2
Output
1 2 3
-1
4 5
1 2 3
4 5 | instruction | 0 | 107,850 | 12 | 215,700 |
"Correct Solution:
```
from collections import deque
n, q = list(map(int, input().split()))
A = deque()
[A.append([]) for _ in range(n)]
for i in range(q):
query = list(map(int, input().split()))
t = query[1]
# pushBack
if query[0] == 0:
x = query[2]
A[t].append(x)
# dump
elif query[0] == 1:
print(*A[t])
# clear
else:
if len(A[t]) != 0:
A[t].clear()
``` | output | 1 | 107,850 | 12 | 215,701 |
Provide a correct Python 3 solution for this coding contest problem.
For $n$ dynamic arrays $A_i$ ($i = 0, 1, ..., n-1$), perform a sequence of the following operations:
* pushBack($t$, $x$): Add element $x$ at the end of $A_t$.
* dump($t$): Print all elements in $A_t$.
* clear($t$): Clear $A_t$. If $A_t$ is empty, do nothing.
$A_i$ is a 0-origin array and it is empty in the initial state.
Constraints
* $1 \leq n \leq 1,000$
* $1 \leq q \leq 500,000$
* $-1,000,000,000 \leq x \leq 1,000,000,000$
* The total number of elements printed by dump operations do not exceed 500,000
Input
The input is given in the following format.
$n$ $q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $t$ $x$
or
1 $t$
or
2 $t$
where the first digits 0, 1 and 2 represent pushBack, dump and clear operations respectively.
Output
For each dump operation, print elements of $A_t$ a line. Separete adjacency elements by a space character (do not print the space after the last element). Note that, if the array is empty, an empty line should be printed.
Example
Input
3 13
0 0 1
0 0 2
0 0 3
0 1 -1
0 2 4
0 2 5
1 0
1 1
1 2
2 1
1 0
1 1
1 2
Output
1 2 3
-1
4 5
1 2 3
4 5 | instruction | 0 | 107,851 | 12 | 215,702 |
"Correct Solution:
```
def main():
n, q = map(int, input().split())
At = list()
for i in range(n):
At.append(list())
for _ in range(q):
param = [int(a) for a in input().split()]
if param[0] == 0:
At[param[1]].append(param[2])
elif param[0] == 1:
if len(At[param[1]]) == 0:
print()
else:
print(*At[param[1]])
elif param[0] == 2:
if len(At[param[1]]) == 0:
continue
else:
At[param[1]].clear()
main()
``` | output | 1 | 107,851 | 12 | 215,703 |
Provide a correct Python 3 solution for this coding contest problem.
For $n$ dynamic arrays $A_i$ ($i = 0, 1, ..., n-1$), perform a sequence of the following operations:
* pushBack($t$, $x$): Add element $x$ at the end of $A_t$.
* dump($t$): Print all elements in $A_t$.
* clear($t$): Clear $A_t$. If $A_t$ is empty, do nothing.
$A_i$ is a 0-origin array and it is empty in the initial state.
Constraints
* $1 \leq n \leq 1,000$
* $1 \leq q \leq 500,000$
* $-1,000,000,000 \leq x \leq 1,000,000,000$
* The total number of elements printed by dump operations do not exceed 500,000
Input
The input is given in the following format.
$n$ $q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $t$ $x$
or
1 $t$
or
2 $t$
where the first digits 0, 1 and 2 represent pushBack, dump and clear operations respectively.
Output
For each dump operation, print elements of $A_t$ a line. Separete adjacency elements by a space character (do not print the space after the last element). Note that, if the array is empty, an empty line should be printed.
Example
Input
3 13
0 0 1
0 0 2
0 0 3
0 1 -1
0 2 4
0 2 5
1 0
1 1
1 2
2 1
1 0
1 1
1 2
Output
1 2 3
-1
4 5
1 2 3
4 5 | instruction | 0 | 107,853 | 12 | 215,706 |
"Correct Solution:
```
#0:pushBack
def pushBack(t,x):
A[t].append(x)
#1:dump
def dump(t):
if len(A[t]) > 0:
print(A[t][0],end="")
for i in A[t][1:]:
print(" {}".format(i), end="")
print()
#2:clear
def clear(t):
A[t].clear()
cmdList = [ pushBack, dump, clear ]
n,q = map(int,input().split())
A = list()
for i in range(n):
A.append([])
for i in range(q):
cmd = input()
if cmd.startswith("0"):
c,t,x = map(int,cmd.split(" "))
cmdList[0](t,x)
if cmd.startswith("1"):
c,t = map(int,cmd.split(" "))
cmdList[1](t)
if cmd.startswith("2"):
c,t = map(int,cmd.split(" "))
cmdList[2](t)
``` | output | 1 | 107,853 | 12 | 215,707 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For $n$ dynamic arrays $A_i$ ($i = 0, 1, ..., n-1$), perform a sequence of the following operations:
* pushBack($t$, $x$): Add element $x$ at the end of $A_t$.
* dump($t$): Print all elements in $A_t$.
* clear($t$): Clear $A_t$. If $A_t$ is empty, do nothing.
$A_i$ is a 0-origin array and it is empty in the initial state.
Constraints
* $1 \leq n \leq 1,000$
* $1 \leq q \leq 500,000$
* $-1,000,000,000 \leq x \leq 1,000,000,000$
* The total number of elements printed by dump operations do not exceed 500,000
Input
The input is given in the following format.
$n$ $q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $t$ $x$
or
1 $t$
or
2 $t$
where the first digits 0, 1 and 2 represent pushBack, dump and clear operations respectively.
Output
For each dump operation, print elements of $A_t$ a line. Separete adjacency elements by a space character (do not print the space after the last element). Note that, if the array is empty, an empty line should be printed.
Example
Input
3 13
0 0 1
0 0 2
0 0 3
0 1 -1
0 2 4
0 2 5
1 0
1 1
1 2
2 1
1 0
1 1
1 2
Output
1 2 3
-1
4 5
1 2 3
4 5
Submitted Solution:
```
# -*- coding: utf-8 -*-
"""
Dynamic Arrays and List - Vector II
http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP2_1_D&lang=jp
"""
n, q = map(int, input().split())
A = [[] for _ in range(n)]
for _ in range(q):
op, t, x = (input() + ' 1').split()[:3]
if op == '0':
A[int(t)].append(x)
elif op == '1':
print(*A[int(t)])
else:
A[int(t)] = []
``` | instruction | 0 | 107,854 | 12 | 215,708 |
Yes | output | 1 | 107,854 | 12 | 215,709 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For $n$ dynamic arrays $A_i$ ($i = 0, 1, ..., n-1$), perform a sequence of the following operations:
* pushBack($t$, $x$): Add element $x$ at the end of $A_t$.
* dump($t$): Print all elements in $A_t$.
* clear($t$): Clear $A_t$. If $A_t$ is empty, do nothing.
$A_i$ is a 0-origin array and it is empty in the initial state.
Constraints
* $1 \leq n \leq 1,000$
* $1 \leq q \leq 500,000$
* $-1,000,000,000 \leq x \leq 1,000,000,000$
* The total number of elements printed by dump operations do not exceed 500,000
Input
The input is given in the following format.
$n$ $q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $t$ $x$
or
1 $t$
or
2 $t$
where the first digits 0, 1 and 2 represent pushBack, dump and clear operations respectively.
Output
For each dump operation, print elements of $A_t$ a line. Separete adjacency elements by a space character (do not print the space after the last element). Note that, if the array is empty, an empty line should be printed.
Example
Input
3 13
0 0 1
0 0 2
0 0 3
0 1 -1
0 2 4
0 2 5
1 0
1 1
1 2
2 1
1 0
1 1
1 2
Output
1 2 3
-1
4 5
1 2 3
4 5
Submitted Solution:
```
# AOJ ITP2_1_D: Vector II
# Python3 2018.6.24 bal4u
from collections import deque
n, q = map(int, input().split())
Q = []
for i in range(n): Q.append(deque())
for i in range(q):
a = input().split()
t = int(a[1])
if a[0] == '0': Q[t].append(a[2]) # pushBack
elif a[0] == '1': print(*Q[t]) # dump
else: Q[t].clear() # clear
``` | instruction | 0 | 107,855 | 12 | 215,710 |
Yes | output | 1 | 107,855 | 12 | 215,711 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For $n$ dynamic arrays $A_i$ ($i = 0, 1, ..., n-1$), perform a sequence of the following operations:
* pushBack($t$, $x$): Add element $x$ at the end of $A_t$.
* dump($t$): Print all elements in $A_t$.
* clear($t$): Clear $A_t$. If $A_t$ is empty, do nothing.
$A_i$ is a 0-origin array and it is empty in the initial state.
Constraints
* $1 \leq n \leq 1,000$
* $1 \leq q \leq 500,000$
* $-1,000,000,000 \leq x \leq 1,000,000,000$
* The total number of elements printed by dump operations do not exceed 500,000
Input
The input is given in the following format.
$n$ $q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $t$ $x$
or
1 $t$
or
2 $t$
where the first digits 0, 1 and 2 represent pushBack, dump and clear operations respectively.
Output
For each dump operation, print elements of $A_t$ a line. Separete adjacency elements by a space character (do not print the space after the last element). Note that, if the array is empty, an empty line should be printed.
Example
Input
3 13
0 0 1
0 0 2
0 0 3
0 1 -1
0 2 4
0 2 5
1 0
1 1
1 2
2 1
1 0
1 1
1 2
Output
1 2 3
-1
4 5
1 2 3
4 5
Submitted Solution:
```
n, q = list(map(int, input().split(' ')))
stacks = [[] for i in range(n)]
for i in range(q):
op = list(map(int, input().split(' ')))
if op[0] == 0:
stacks[op[1]].append(op[2])
elif op[0] == 1:
print(' '.join(list(map(str, stacks[op[1]]))))
elif op[0] == 2:
stacks[op[1]] = []
``` | instruction | 0 | 107,856 | 12 | 215,712 |
Yes | output | 1 | 107,856 | 12 | 215,713 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For $n$ dynamic arrays $A_i$ ($i = 0, 1, ..., n-1$), perform a sequence of the following operations:
* pushBack($t$, $x$): Add element $x$ at the end of $A_t$.
* dump($t$): Print all elements in $A_t$.
* clear($t$): Clear $A_t$. If $A_t$ is empty, do nothing.
$A_i$ is a 0-origin array and it is empty in the initial state.
Constraints
* $1 \leq n \leq 1,000$
* $1 \leq q \leq 500,000$
* $-1,000,000,000 \leq x \leq 1,000,000,000$
* The total number of elements printed by dump operations do not exceed 500,000
Input
The input is given in the following format.
$n$ $q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $t$ $x$
or
1 $t$
or
2 $t$
where the first digits 0, 1 and 2 represent pushBack, dump and clear operations respectively.
Output
For each dump operation, print elements of $A_t$ a line. Separete adjacency elements by a space character (do not print the space after the last element). Note that, if the array is empty, an empty line should be printed.
Example
Input
3 13
0 0 1
0 0 2
0 0 3
0 1 -1
0 2 4
0 2 5
1 0
1 1
1 2
2 1
1 0
1 1
1 2
Output
1 2 3
-1
4 5
1 2 3
4 5
Submitted Solution:
```
# AOJ ITP2_1_D Vector II
from collections import deque
n, q = map(int, input().split())
Q = []
for i in range(n):
Q.append(deque())
for i in range(q):
a = input().split()
t = int(a[1])
if a[0] == '0':
Q[t].append(a[2])
elif a[0] == '1':
print(*Q[t])
else:
Q[t].clear()
``` | instruction | 0 | 107,857 | 12 | 215,714 |
Yes | output | 1 | 107,857 | 12 | 215,715 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Recently, on the course of algorithms and data structures, Valeriy learned how to use a deque. He built a deque filled with n elements. The i-th element is a_i (i = 1, 2, …, n). He gradually takes the first two leftmost elements from the deque (let's call them A and B, respectively), and then does the following: if A > B, he writes A to the beginning and writes B to the end of the deque, otherwise, he writes to the beginning B, and A writes to the end of the deque. We call this sequence of actions an operation.
For example, if deque was [2, 3, 4, 5, 1], on the operation he will write B=3 to the beginning and A=2 to the end, so he will get [3, 4, 5, 1, 2].
The teacher of the course, seeing Valeriy, who was passionate about his work, approached him and gave him q queries. Each query consists of the singular number m_j (j = 1, 2, …, q). It is required for each query to answer which two elements he will pull out on the m_j-th operation.
Note that the queries are independent and for each query the numbers A and B should be printed in the order in which they will be pulled out of the deque.
Deque is a data structure representing a list of elements where insertion of new elements or deletion of existing elements can be made from both sides.
Input
The first line contains two integers n and q (2 ≤ n ≤ 10^5, 0 ≤ q ≤ 3 ⋅ 10^5) — the number of elements in the deque and the number of queries. The second line contains n integers a_1, a_2, ..., a_n, where a_i (0 ≤ a_i ≤ 10^9) — the deque element in i-th position. The next q lines contain one number each, meaning m_j (1 ≤ m_j ≤ 10^{18}).
Output
For each teacher's query, output two numbers A and B — the numbers that Valeriy pulls out of the deque for the m_j-th operation.
Examples
Input
5 3
1 2 3 4 5
1
2
10
Output
1 2
2 3
5 2
Input
2 0
0 0
Output
Note
Consider all 10 steps for the first test in detail:
1. [1, 2, 3, 4, 5] — on the first operation, A and B are 1 and 2, respectively.
So, 2 we write to the beginning of the deque, and 1 — to the end.
We get the following status of the deque: [2, 3, 4, 5, 1].
2. [2, 3, 4, 5, 1] ⇒ A = 2, B = 3.
3. [3, 4, 5, 1, 2]
4. [4, 5, 1, 2, 3]
5. [5, 1, 2, 3, 4]
6. [5, 2, 3, 4, 1]
7. [5, 3, 4, 1, 2]
8. [5, 4, 1, 2, 3]
9. [5, 1, 2, 3, 4]
10. [5, 2, 3, 4, 1] ⇒ A = 5, B = 2. | instruction | 0 | 107,898 | 12 | 215,796 |
Tags: data structures, implementation
Correct Solution:
```
[n,q] = list(map(int , input().split()))
a = list(map(int , input().split()))
qry = [0 for i in range(q)]
for i in range(q):
qry[i] = int(input())
ans = [[-1,-1]]
m = max(a)
idx = a.index(m)
#print("idx = {}, m = {}".format(idx,m))
#print(a)
#t1 = min(a[0],a[1])
t1 = a[0]
for i in range(idx):
ans.append([t1,a[i+1]])
a.append(min(t1,a[i+1]))
t1 = max(a[i+1],t1)
#print(a)
for i in range(q):
if (qry[i] <= idx):
print(ans[qry[i]][0] , end=" ")
print(ans[qry[i]][1])
else:
print(t1,end = " ")
print(a[ (idx + 1 + (qry[i]-idx-1)%(n-1) ) ])
``` | output | 1 | 107,898 | 12 | 215,797 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Recently, on the course of algorithms and data structures, Valeriy learned how to use a deque. He built a deque filled with n elements. The i-th element is a_i (i = 1, 2, …, n). He gradually takes the first two leftmost elements from the deque (let's call them A and B, respectively), and then does the following: if A > B, he writes A to the beginning and writes B to the end of the deque, otherwise, he writes to the beginning B, and A writes to the end of the deque. We call this sequence of actions an operation.
For example, if deque was [2, 3, 4, 5, 1], on the operation he will write B=3 to the beginning and A=2 to the end, so he will get [3, 4, 5, 1, 2].
The teacher of the course, seeing Valeriy, who was passionate about his work, approached him and gave him q queries. Each query consists of the singular number m_j (j = 1, 2, …, q). It is required for each query to answer which two elements he will pull out on the m_j-th operation.
Note that the queries are independent and for each query the numbers A and B should be printed in the order in which they will be pulled out of the deque.
Deque is a data structure representing a list of elements where insertion of new elements or deletion of existing elements can be made from both sides.
Input
The first line contains two integers n and q (2 ≤ n ≤ 10^5, 0 ≤ q ≤ 3 ⋅ 10^5) — the number of elements in the deque and the number of queries. The second line contains n integers a_1, a_2, ..., a_n, where a_i (0 ≤ a_i ≤ 10^9) — the deque element in i-th position. The next q lines contain one number each, meaning m_j (1 ≤ m_j ≤ 10^{18}).
Output
For each teacher's query, output two numbers A and B — the numbers that Valeriy pulls out of the deque for the m_j-th operation.
Examples
Input
5 3
1 2 3 4 5
1
2
10
Output
1 2
2 3
5 2
Input
2 0
0 0
Output
Note
Consider all 10 steps for the first test in detail:
1. [1, 2, 3, 4, 5] — on the first operation, A and B are 1 and 2, respectively.
So, 2 we write to the beginning of the deque, and 1 — to the end.
We get the following status of the deque: [2, 3, 4, 5, 1].
2. [2, 3, 4, 5, 1] ⇒ A = 2, B = 3.
3. [3, 4, 5, 1, 2]
4. [4, 5, 1, 2, 3]
5. [5, 1, 2, 3, 4]
6. [5, 2, 3, 4, 1]
7. [5, 3, 4, 1, 2]
8. [5, 4, 1, 2, 3]
9. [5, 1, 2, 3, 4]
10. [5, 2, 3, 4, 1] ⇒ A = 5, B = 2. | instruction | 0 | 107,899 | 12 | 215,798 |
Tags: data structures, implementation
Correct Solution:
```
from collections import deque
n,q = map(int,input().split())
a = deque(list(map(int,input().split())))
M = [int(input()) for i in range(q)]
m = sorted([ M[i] for i in range(q)])
d = []
if q == 0:
exit()
ma = max(a)
c = 0
cnt = 0
for i in range(n):
if a[0] == ma:
break
A = a.popleft()
B = a.popleft()
d.append([A,B])
if A > B:
a.appendleft(A)
a.append(B)
else:
a.appendleft(B)
a.append(A)
cnt += 1
cnt += 1
for i in range(c,q):
if M[i] >= cnt:
print(ma, a[1 + ((M[i] - cnt) % (n-1))])
else:
print(d[M[i]-1][0],d[M[i]-1][1])
``` | output | 1 | 107,899 | 12 | 215,799 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Recently, on the course of algorithms and data structures, Valeriy learned how to use a deque. He built a deque filled with n elements. The i-th element is a_i (i = 1, 2, …, n). He gradually takes the first two leftmost elements from the deque (let's call them A and B, respectively), and then does the following: if A > B, he writes A to the beginning and writes B to the end of the deque, otherwise, he writes to the beginning B, and A writes to the end of the deque. We call this sequence of actions an operation.
For example, if deque was [2, 3, 4, 5, 1], on the operation he will write B=3 to the beginning and A=2 to the end, so he will get [3, 4, 5, 1, 2].
The teacher of the course, seeing Valeriy, who was passionate about his work, approached him and gave him q queries. Each query consists of the singular number m_j (j = 1, 2, …, q). It is required for each query to answer which two elements he will pull out on the m_j-th operation.
Note that the queries are independent and for each query the numbers A and B should be printed in the order in which they will be pulled out of the deque.
Deque is a data structure representing a list of elements where insertion of new elements or deletion of existing elements can be made from both sides.
Input
The first line contains two integers n and q (2 ≤ n ≤ 10^5, 0 ≤ q ≤ 3 ⋅ 10^5) — the number of elements in the deque and the number of queries. The second line contains n integers a_1, a_2, ..., a_n, where a_i (0 ≤ a_i ≤ 10^9) — the deque element in i-th position. The next q lines contain one number each, meaning m_j (1 ≤ m_j ≤ 10^{18}).
Output
For each teacher's query, output two numbers A and B — the numbers that Valeriy pulls out of the deque for the m_j-th operation.
Examples
Input
5 3
1 2 3 4 5
1
2
10
Output
1 2
2 3
5 2
Input
2 0
0 0
Output
Note
Consider all 10 steps for the first test in detail:
1. [1, 2, 3, 4, 5] — on the first operation, A and B are 1 and 2, respectively.
So, 2 we write to the beginning of the deque, and 1 — to the end.
We get the following status of the deque: [2, 3, 4, 5, 1].
2. [2, 3, 4, 5, 1] ⇒ A = 2, B = 3.
3. [3, 4, 5, 1, 2]
4. [4, 5, 1, 2, 3]
5. [5, 1, 2, 3, 4]
6. [5, 2, 3, 4, 1]
7. [5, 3, 4, 1, 2]
8. [5, 4, 1, 2, 3]
9. [5, 1, 2, 3, 4]
10. [5, 2, 3, 4, 1] ⇒ A = 5, B = 2. | instruction | 0 | 107,900 | 12 | 215,800 |
Tags: data structures, implementation
Correct Solution:
```
import sys
import math
input = sys.stdin.readline
n,q=map(int,input().split())
arr=list(map(int,input().split()))
for i in range(n):
arr.append(0)
maxx=0
ind=arr.index(max(arr))
ans=[]
ptr1=0
ptr2=n
for i in range(ind):
ans.append([arr[ptr1],arr[ptr1+1]])
if arr[ptr1]>arr[ptr1+1]:
arr[ptr2]=arr[ptr1+1]
arr[ptr1+1]=arr[ptr1]
else:
arr[ptr2]=arr[ptr1]
ptr1+=1
ptr2+=1
#print(arr)
for i in range(q):
m=int(input())
if m<=ind:
print(*ans[m-1])
else:
m-=ind
m=m%(n-1)
if m==0:
m+=n-1
print(arr[ind],arr[ind+m])
``` | output | 1 | 107,900 | 12 | 215,801 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Recently, on the course of algorithms and data structures, Valeriy learned how to use a deque. He built a deque filled with n elements. The i-th element is a_i (i = 1, 2, …, n). He gradually takes the first two leftmost elements from the deque (let's call them A and B, respectively), and then does the following: if A > B, he writes A to the beginning and writes B to the end of the deque, otherwise, he writes to the beginning B, and A writes to the end of the deque. We call this sequence of actions an operation.
For example, if deque was [2, 3, 4, 5, 1], on the operation he will write B=3 to the beginning and A=2 to the end, so he will get [3, 4, 5, 1, 2].
The teacher of the course, seeing Valeriy, who was passionate about his work, approached him and gave him q queries. Each query consists of the singular number m_j (j = 1, 2, …, q). It is required for each query to answer which two elements he will pull out on the m_j-th operation.
Note that the queries are independent and for each query the numbers A and B should be printed in the order in which they will be pulled out of the deque.
Deque is a data structure representing a list of elements where insertion of new elements or deletion of existing elements can be made from both sides.
Input
The first line contains two integers n and q (2 ≤ n ≤ 10^5, 0 ≤ q ≤ 3 ⋅ 10^5) — the number of elements in the deque and the number of queries. The second line contains n integers a_1, a_2, ..., a_n, where a_i (0 ≤ a_i ≤ 10^9) — the deque element in i-th position. The next q lines contain one number each, meaning m_j (1 ≤ m_j ≤ 10^{18}).
Output
For each teacher's query, output two numbers A and B — the numbers that Valeriy pulls out of the deque for the m_j-th operation.
Examples
Input
5 3
1 2 3 4 5
1
2
10
Output
1 2
2 3
5 2
Input
2 0
0 0
Output
Note
Consider all 10 steps for the first test in detail:
1. [1, 2, 3, 4, 5] — on the first operation, A and B are 1 and 2, respectively.
So, 2 we write to the beginning of the deque, and 1 — to the end.
We get the following status of the deque: [2, 3, 4, 5, 1].
2. [2, 3, 4, 5, 1] ⇒ A = 2, B = 3.
3. [3, 4, 5, 1, 2]
4. [4, 5, 1, 2, 3]
5. [5, 1, 2, 3, 4]
6. [5, 2, 3, 4, 1]
7. [5, 3, 4, 1, 2]
8. [5, 4, 1, 2, 3]
9. [5, 1, 2, 3, 4]
10. [5, 2, 3, 4, 1] ⇒ A = 5, B = 2. | instruction | 0 | 107,901 | 12 | 215,802 |
Tags: data structures, implementation
Correct Solution:
```
import sys
input = sys.stdin.readline
from collections import deque
N, Q = map(int, input().split())
que = deque([int(a) for a in input().split()])
ma = max(que)
X = []
k = -1
c = 0
while c <= k+N+5:
a = deque.popleft(que)
b = deque.popleft(que)
X.append((a, b))
c += 1
if a > b:
a, b = b, a
if k < 0 and b == ma:
k = c
deque.appendleft(que, b)
deque.append(que, a)
for _ in range(Q):
i = int(input()) - 1
if i <= k:
print(*X[i])
else:
i = (i-k)%(N-1)+k
print(*X[i])
``` | output | 1 | 107,901 | 12 | 215,803 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Recently, on the course of algorithms and data structures, Valeriy learned how to use a deque. He built a deque filled with n elements. The i-th element is a_i (i = 1, 2, …, n). He gradually takes the first two leftmost elements from the deque (let's call them A and B, respectively), and then does the following: if A > B, he writes A to the beginning and writes B to the end of the deque, otherwise, he writes to the beginning B, and A writes to the end of the deque. We call this sequence of actions an operation.
For example, if deque was [2, 3, 4, 5, 1], on the operation he will write B=3 to the beginning and A=2 to the end, so he will get [3, 4, 5, 1, 2].
The teacher of the course, seeing Valeriy, who was passionate about his work, approached him and gave him q queries. Each query consists of the singular number m_j (j = 1, 2, …, q). It is required for each query to answer which two elements he will pull out on the m_j-th operation.
Note that the queries are independent and for each query the numbers A and B should be printed in the order in which they will be pulled out of the deque.
Deque is a data structure representing a list of elements where insertion of new elements or deletion of existing elements can be made from both sides.
Input
The first line contains two integers n and q (2 ≤ n ≤ 10^5, 0 ≤ q ≤ 3 ⋅ 10^5) — the number of elements in the deque and the number of queries. The second line contains n integers a_1, a_2, ..., a_n, where a_i (0 ≤ a_i ≤ 10^9) — the deque element in i-th position. The next q lines contain one number each, meaning m_j (1 ≤ m_j ≤ 10^{18}).
Output
For each teacher's query, output two numbers A and B — the numbers that Valeriy pulls out of the deque for the m_j-th operation.
Examples
Input
5 3
1 2 3 4 5
1
2
10
Output
1 2
2 3
5 2
Input
2 0
0 0
Output
Note
Consider all 10 steps for the first test in detail:
1. [1, 2, 3, 4, 5] — on the first operation, A and B are 1 and 2, respectively.
So, 2 we write to the beginning of the deque, and 1 — to the end.
We get the following status of the deque: [2, 3, 4, 5, 1].
2. [2, 3, 4, 5, 1] ⇒ A = 2, B = 3.
3. [3, 4, 5, 1, 2]
4. [4, 5, 1, 2, 3]
5. [5, 1, 2, 3, 4]
6. [5, 2, 3, 4, 1]
7. [5, 3, 4, 1, 2]
8. [5, 4, 1, 2, 3]
9. [5, 1, 2, 3, 4]
10. [5, 2, 3, 4, 1] ⇒ A = 5, B = 2. | instruction | 0 | 107,902 | 12 | 215,804 |
Tags: data structures, implementation
Correct Solution:
```
from collections import deque
n,q = list(map(int,input().split()))
a = list(map(int,input().split()))
maxx = max(a)
maxidx = a.index(maxx)
out = {}
left = maxidx
a = deque(a)
while left:
a1 = a.popleft()
b1 = a.popleft()
out[maxidx-left+1]=(a1,b1)
if a1>b1:
a.appendleft(a1)
a.append(b1)
else:
a.appendleft(b1)
a.append(a1)
left-=1
# print(a)
a = list(a)[1:]
# print(a)
for i in range(q):
curq = int(input())
if curq<=maxidx:
print(*out[curq])
else:
curq-=maxidx
pos = curq%(n-1)-1
print(maxx,a[pos])
``` | output | 1 | 107,902 | 12 | 215,805 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Recently, on the course of algorithms and data structures, Valeriy learned how to use a deque. He built a deque filled with n elements. The i-th element is a_i (i = 1, 2, …, n). He gradually takes the first two leftmost elements from the deque (let's call them A and B, respectively), and then does the following: if A > B, he writes A to the beginning and writes B to the end of the deque, otherwise, he writes to the beginning B, and A writes to the end of the deque. We call this sequence of actions an operation.
For example, if deque was [2, 3, 4, 5, 1], on the operation he will write B=3 to the beginning and A=2 to the end, so he will get [3, 4, 5, 1, 2].
The teacher of the course, seeing Valeriy, who was passionate about his work, approached him and gave him q queries. Each query consists of the singular number m_j (j = 1, 2, …, q). It is required for each query to answer which two elements he will pull out on the m_j-th operation.
Note that the queries are independent and for each query the numbers A and B should be printed in the order in which they will be pulled out of the deque.
Deque is a data structure representing a list of elements where insertion of new elements or deletion of existing elements can be made from both sides.
Input
The first line contains two integers n and q (2 ≤ n ≤ 10^5, 0 ≤ q ≤ 3 ⋅ 10^5) — the number of elements in the deque and the number of queries. The second line contains n integers a_1, a_2, ..., a_n, where a_i (0 ≤ a_i ≤ 10^9) — the deque element in i-th position. The next q lines contain one number each, meaning m_j (1 ≤ m_j ≤ 10^{18}).
Output
For each teacher's query, output two numbers A and B — the numbers that Valeriy pulls out of the deque for the m_j-th operation.
Examples
Input
5 3
1 2 3 4 5
1
2
10
Output
1 2
2 3
5 2
Input
2 0
0 0
Output
Note
Consider all 10 steps for the first test in detail:
1. [1, 2, 3, 4, 5] — on the first operation, A and B are 1 and 2, respectively.
So, 2 we write to the beginning of the deque, and 1 — to the end.
We get the following status of the deque: [2, 3, 4, 5, 1].
2. [2, 3, 4, 5, 1] ⇒ A = 2, B = 3.
3. [3, 4, 5, 1, 2]
4. [4, 5, 1, 2, 3]
5. [5, 1, 2, 3, 4]
6. [5, 2, 3, 4, 1]
7. [5, 3, 4, 1, 2]
8. [5, 4, 1, 2, 3]
9. [5, 1, 2, 3, 4]
10. [5, 2, 3, 4, 1] ⇒ A = 5, B = 2. | instruction | 0 | 107,903 | 12 | 215,806 |
Tags: data structures, implementation
Correct Solution:
```
import collections
n,q=list(map(int,input().split()))
l=[int(x) for x in input().split()]
d = collections.deque(l)
dd=d.copy()
g=max(d)
ind=l.index(g)
ans=[]
s=''
for i in range(ind+n-1):
ans.append([str(d[0]),str(d[1])])
a=max(d[0],d[1])
b=min(d[0],d[1])
d.popleft()
d.popleft()
d.appendleft(a)
d.append(b)
for i in range(q):
t=int(input())
if t<ind+n-1:
s=' '.join(ans[t-1])
else:
t=(t-ind)%(n-1)
if t==0:
t=ind+n-2
else:
t+=ind-1
s=' '.join(ans[t])
print(s)
``` | output | 1 | 107,903 | 12 | 215,807 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Recently, on the course of algorithms and data structures, Valeriy learned how to use a deque. He built a deque filled with n elements. The i-th element is a_i (i = 1, 2, …, n). He gradually takes the first two leftmost elements from the deque (let's call them A and B, respectively), and then does the following: if A > B, he writes A to the beginning and writes B to the end of the deque, otherwise, he writes to the beginning B, and A writes to the end of the deque. We call this sequence of actions an operation.
For example, if deque was [2, 3, 4, 5, 1], on the operation he will write B=3 to the beginning and A=2 to the end, so he will get [3, 4, 5, 1, 2].
The teacher of the course, seeing Valeriy, who was passionate about his work, approached him and gave him q queries. Each query consists of the singular number m_j (j = 1, 2, …, q). It is required for each query to answer which two elements he will pull out on the m_j-th operation.
Note that the queries are independent and for each query the numbers A and B should be printed in the order in which they will be pulled out of the deque.
Deque is a data structure representing a list of elements where insertion of new elements or deletion of existing elements can be made from both sides.
Input
The first line contains two integers n and q (2 ≤ n ≤ 10^5, 0 ≤ q ≤ 3 ⋅ 10^5) — the number of elements in the deque and the number of queries. The second line contains n integers a_1, a_2, ..., a_n, where a_i (0 ≤ a_i ≤ 10^9) — the deque element in i-th position. The next q lines contain one number each, meaning m_j (1 ≤ m_j ≤ 10^{18}).
Output
For each teacher's query, output two numbers A and B — the numbers that Valeriy pulls out of the deque for the m_j-th operation.
Examples
Input
5 3
1 2 3 4 5
1
2
10
Output
1 2
2 3
5 2
Input
2 0
0 0
Output
Note
Consider all 10 steps for the first test in detail:
1. [1, 2, 3, 4, 5] — on the first operation, A and B are 1 and 2, respectively.
So, 2 we write to the beginning of the deque, and 1 — to the end.
We get the following status of the deque: [2, 3, 4, 5, 1].
2. [2, 3, 4, 5, 1] ⇒ A = 2, B = 3.
3. [3, 4, 5, 1, 2]
4. [4, 5, 1, 2, 3]
5. [5, 1, 2, 3, 4]
6. [5, 2, 3, 4, 1]
7. [5, 3, 4, 1, 2]
8. [5, 4, 1, 2, 3]
9. [5, 1, 2, 3, 4]
10. [5, 2, 3, 4, 1] ⇒ A = 5, B = 2. | instruction | 0 | 107,904 | 12 | 215,808 |
Tags: data structures, implementation
Correct Solution:
```
import collections
n, q = map(int, input().split(' '))
d = collections.deque([*map(int, input().split(' '))])
h = [[]]
for _ in range(2 * n + 1):
a, b = d.popleft(), d.popleft()
h.append([a, b])
if a > b:
d.appendleft(a)
d.append(b)
else:
d.appendleft(b)
d.append(a)
for _ in range(q):
num = int(input())
if num <= n:
print(*h[num])
else:
idx = (num - n) % (n - 1) + n
print(*h[idx])
``` | output | 1 | 107,904 | 12 | 215,809 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Recently, on the course of algorithms and data structures, Valeriy learned how to use a deque. He built a deque filled with n elements. The i-th element is a_i (i = 1, 2, …, n). He gradually takes the first two leftmost elements from the deque (let's call them A and B, respectively), and then does the following: if A > B, he writes A to the beginning and writes B to the end of the deque, otherwise, he writes to the beginning B, and A writes to the end of the deque. We call this sequence of actions an operation.
For example, if deque was [2, 3, 4, 5, 1], on the operation he will write B=3 to the beginning and A=2 to the end, so he will get [3, 4, 5, 1, 2].
The teacher of the course, seeing Valeriy, who was passionate about his work, approached him and gave him q queries. Each query consists of the singular number m_j (j = 1, 2, …, q). It is required for each query to answer which two elements he will pull out on the m_j-th operation.
Note that the queries are independent and for each query the numbers A and B should be printed in the order in which they will be pulled out of the deque.
Deque is a data structure representing a list of elements where insertion of new elements or deletion of existing elements can be made from both sides.
Input
The first line contains two integers n and q (2 ≤ n ≤ 10^5, 0 ≤ q ≤ 3 ⋅ 10^5) — the number of elements in the deque and the number of queries. The second line contains n integers a_1, a_2, ..., a_n, where a_i (0 ≤ a_i ≤ 10^9) — the deque element in i-th position. The next q lines contain one number each, meaning m_j (1 ≤ m_j ≤ 10^{18}).
Output
For each teacher's query, output two numbers A and B — the numbers that Valeriy pulls out of the deque for the m_j-th operation.
Examples
Input
5 3
1 2 3 4 5
1
2
10
Output
1 2
2 3
5 2
Input
2 0
0 0
Output
Note
Consider all 10 steps for the first test in detail:
1. [1, 2, 3, 4, 5] — on the first operation, A and B are 1 and 2, respectively.
So, 2 we write to the beginning of the deque, and 1 — to the end.
We get the following status of the deque: [2, 3, 4, 5, 1].
2. [2, 3, 4, 5, 1] ⇒ A = 2, B = 3.
3. [3, 4, 5, 1, 2]
4. [4, 5, 1, 2, 3]
5. [5, 1, 2, 3, 4]
6. [5, 2, 3, 4, 1]
7. [5, 3, 4, 1, 2]
8. [5, 4, 1, 2, 3]
9. [5, 1, 2, 3, 4]
10. [5, 2, 3, 4, 1] ⇒ A = 5, B = 2. | instruction | 0 | 107,905 | 12 | 215,810 |
Tags: data structures, implementation
Correct Solution:
```
from collections import deque
inp = list(map(int, input().split(" ")))
N = int(inp[0])
q = int(inp[1])
A = list(map(int, input().split(" ")))
d = deque(A)
ans = [[] for i in range(N)]
for i in range(N - 1):
a = d.popleft()
b = d.popleft()
ans[i].append(a)
ans[i].append(b)
if(a > b):
d.appendleft(a)
d.append(b)
else:
d.appendleft(b)
d.append(a)
for i in range(q):
m = int(input())
if(m < N):
print(ans[m - 1][0], ans[m - 1][1])
else:
ind = m % (N - 1)
# print(ind)
# print(d)
if(ind == 0):
ind = N - 1
print(d[0], d[ind])
``` | output | 1 | 107,905 | 12 | 215,811 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Recently, on the course of algorithms and data structures, Valeriy learned how to use a deque. He built a deque filled with n elements. The i-th element is a_i (i = 1, 2, …, n). He gradually takes the first two leftmost elements from the deque (let's call them A and B, respectively), and then does the following: if A > B, he writes A to the beginning and writes B to the end of the deque, otherwise, he writes to the beginning B, and A writes to the end of the deque. We call this sequence of actions an operation.
For example, if deque was [2, 3, 4, 5, 1], on the operation he will write B=3 to the beginning and A=2 to the end, so he will get [3, 4, 5, 1, 2].
The teacher of the course, seeing Valeriy, who was passionate about his work, approached him and gave him q queries. Each query consists of the singular number m_j (j = 1, 2, …, q). It is required for each query to answer which two elements he will pull out on the m_j-th operation.
Note that the queries are independent and for each query the numbers A and B should be printed in the order in which they will be pulled out of the deque.
Deque is a data structure representing a list of elements where insertion of new elements or deletion of existing elements can be made from both sides.
Input
The first line contains two integers n and q (2 ≤ n ≤ 10^5, 0 ≤ q ≤ 3 ⋅ 10^5) — the number of elements in the deque and the number of queries. The second line contains n integers a_1, a_2, ..., a_n, where a_i (0 ≤ a_i ≤ 10^9) — the deque element in i-th position. The next q lines contain one number each, meaning m_j (1 ≤ m_j ≤ 10^{18}).
Output
For each teacher's query, output two numbers A and B — the numbers that Valeriy pulls out of the deque for the m_j-th operation.
Examples
Input
5 3
1 2 3 4 5
1
2
10
Output
1 2
2 3
5 2
Input
2 0
0 0
Output
Note
Consider all 10 steps for the first test in detail:
1. [1, 2, 3, 4, 5] — on the first operation, A and B are 1 and 2, respectively.
So, 2 we write to the beginning of the deque, and 1 — to the end.
We get the following status of the deque: [2, 3, 4, 5, 1].
2. [2, 3, 4, 5, 1] ⇒ A = 2, B = 3.
3. [3, 4, 5, 1, 2]
4. [4, 5, 1, 2, 3]
5. [5, 1, 2, 3, 4]
6. [5, 2, 3, 4, 1]
7. [5, 3, 4, 1, 2]
8. [5, 4, 1, 2, 3]
9. [5, 1, 2, 3, 4]
10. [5, 2, 3, 4, 1] ⇒ A = 5, B = 2.
Submitted Solution:
```
import io, os
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
from collections import deque
n, q = map(int, input().split())
l = deque(map(int, input().split()))
mx = max(l)
op = [(-1, -1)]
while l[0] != mx:
a = l.popleft()
b = l.popleft()
l.appendleft(max(a, b))
l.append(min(a, b))
op.append((a, b))
for i in range(q):
m = int(input())
if m <= len(op)-1:
print(op[m][0], op[m][1])
else:
print(mx, l[1+((m-len(op))%(n-1))])
``` | instruction | 0 | 107,906 | 12 | 215,812 |
Yes | output | 1 | 107,906 | 12 | 215,813 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Recently, on the course of algorithms and data structures, Valeriy learned how to use a deque. He built a deque filled with n elements. The i-th element is a_i (i = 1, 2, …, n). He gradually takes the first two leftmost elements from the deque (let's call them A and B, respectively), and then does the following: if A > B, he writes A to the beginning and writes B to the end of the deque, otherwise, he writes to the beginning B, and A writes to the end of the deque. We call this sequence of actions an operation.
For example, if deque was [2, 3, 4, 5, 1], on the operation he will write B=3 to the beginning and A=2 to the end, so he will get [3, 4, 5, 1, 2].
The teacher of the course, seeing Valeriy, who was passionate about his work, approached him and gave him q queries. Each query consists of the singular number m_j (j = 1, 2, …, q). It is required for each query to answer which two elements he will pull out on the m_j-th operation.
Note that the queries are independent and for each query the numbers A and B should be printed in the order in which they will be pulled out of the deque.
Deque is a data structure representing a list of elements where insertion of new elements or deletion of existing elements can be made from both sides.
Input
The first line contains two integers n and q (2 ≤ n ≤ 10^5, 0 ≤ q ≤ 3 ⋅ 10^5) — the number of elements in the deque and the number of queries. The second line contains n integers a_1, a_2, ..., a_n, where a_i (0 ≤ a_i ≤ 10^9) — the deque element in i-th position. The next q lines contain one number each, meaning m_j (1 ≤ m_j ≤ 10^{18}).
Output
For each teacher's query, output two numbers A and B — the numbers that Valeriy pulls out of the deque for the m_j-th operation.
Examples
Input
5 3
1 2 3 4 5
1
2
10
Output
1 2
2 3
5 2
Input
2 0
0 0
Output
Note
Consider all 10 steps for the first test in detail:
1. [1, 2, 3, 4, 5] — on the first operation, A and B are 1 and 2, respectively.
So, 2 we write to the beginning of the deque, and 1 — to the end.
We get the following status of the deque: [2, 3, 4, 5, 1].
2. [2, 3, 4, 5, 1] ⇒ A = 2, B = 3.
3. [3, 4, 5, 1, 2]
4. [4, 5, 1, 2, 3]
5. [5, 1, 2, 3, 4]
6. [5, 2, 3, 4, 1]
7. [5, 3, 4, 1, 2]
8. [5, 4, 1, 2, 3]
9. [5, 1, 2, 3, 4]
10. [5, 2, 3, 4, 1] ⇒ A = 5, B = 2.
Submitted Solution:
```
from sys import stdin
def main():
n, m = map(int, input().split())
l = list(map(int, input().split()))
x = max(range(n), key=l.__getitem__) + 1
a, buf = l[0], []
for b in l[1:x + 1]:
buf.append((a, b))
if a < b:
a, b = b, a
l.append(b)
del l[:x]
n -= 1
res = stdin.read().splitlines()
for i, s in enumerate(res):
q = int(s)
res[i] = '%d %d' % ((a, l[(q - x) % n]) if x < q else buf[q - 1])
print('\n'.join(res))
if __name__ == '__main__':
main()
``` | instruction | 0 | 107,907 | 12 | 215,814 |
Yes | output | 1 | 107,907 | 12 | 215,815 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Recently, on the course of algorithms and data structures, Valeriy learned how to use a deque. He built a deque filled with n elements. The i-th element is a_i (i = 1, 2, …, n). He gradually takes the first two leftmost elements from the deque (let's call them A and B, respectively), and then does the following: if A > B, he writes A to the beginning and writes B to the end of the deque, otherwise, he writes to the beginning B, and A writes to the end of the deque. We call this sequence of actions an operation.
For example, if deque was [2, 3, 4, 5, 1], on the operation he will write B=3 to the beginning and A=2 to the end, so he will get [3, 4, 5, 1, 2].
The teacher of the course, seeing Valeriy, who was passionate about his work, approached him and gave him q queries. Each query consists of the singular number m_j (j = 1, 2, …, q). It is required for each query to answer which two elements he will pull out on the m_j-th operation.
Note that the queries are independent and for each query the numbers A and B should be printed in the order in which they will be pulled out of the deque.
Deque is a data structure representing a list of elements where insertion of new elements or deletion of existing elements can be made from both sides.
Input
The first line contains two integers n and q (2 ≤ n ≤ 10^5, 0 ≤ q ≤ 3 ⋅ 10^5) — the number of elements in the deque and the number of queries. The second line contains n integers a_1, a_2, ..., a_n, where a_i (0 ≤ a_i ≤ 10^9) — the deque element in i-th position. The next q lines contain one number each, meaning m_j (1 ≤ m_j ≤ 10^{18}).
Output
For each teacher's query, output two numbers A and B — the numbers that Valeriy pulls out of the deque for the m_j-th operation.
Examples
Input
5 3
1 2 3 4 5
1
2
10
Output
1 2
2 3
5 2
Input
2 0
0 0
Output
Note
Consider all 10 steps for the first test in detail:
1. [1, 2, 3, 4, 5] — on the first operation, A and B are 1 and 2, respectively.
So, 2 we write to the beginning of the deque, and 1 — to the end.
We get the following status of the deque: [2, 3, 4, 5, 1].
2. [2, 3, 4, 5, 1] ⇒ A = 2, B = 3.
3. [3, 4, 5, 1, 2]
4. [4, 5, 1, 2, 3]
5. [5, 1, 2, 3, 4]
6. [5, 2, 3, 4, 1]
7. [5, 3, 4, 1, 2]
8. [5, 4, 1, 2, 3]
9. [5, 1, 2, 3, 4]
10. [5, 2, 3, 4, 1] ⇒ A = 5, B = 2.
Submitted Solution:
```
from collections import deque
if __name__ == "__main__":
n, q = [int(x) for x in input().split(" ")]
elements_queue = [int(x) for x in input().split(" ")]
ans = []
queries = []
max_queries = 0
for i in range(int(q)):
n_op = int(input())
queries.append((n_op,i))
if n_op > max_queries:
max_queries = n_op
queries.sort()
#print(queries)
pointer_curr_query = 0
queue = deque(elements_queue)
max_queue = max(elements_queue)
n_ops_rem = 0
#print(max_queries,"BBBBBBB")
#print(max_queue, "CCC")
first = True
for i in range(max_queries):
if i != 0:
first = False
A = queue.popleft()
B = queue.popleft()
if A > B:
queue.appendleft(A)
queue.append(B)
else:
queue.appendleft(B)
queue.append(A)
while pointer_curr_query < len(queries) and i+1 == queries[pointer_curr_query][0]:
ans.append(([A,B], queries[pointer_curr_query][1]))
pointer_curr_query +=1
if A == max_queue:
if first:
n_ops_rem = 2
break
if B == max_queue:
n_ops_rem = i+2
break
#print(pointer_curr_query, "AAAAAAAAAAA")
while pointer_curr_query < len(queries):
curr_query = queries[pointer_curr_query][0]
ind = (curr_query - n_ops_rem)%(len(queue)-1)
b = queue[ind+1]
ans.append(([max_queue,b],queries[pointer_curr_query][1]))
pointer_curr_query +=1
#print(ans)
ans.sort(key=lambda x:x[1])
#print(ans)
for i in ans:
a = i[0]
print(a[0],a[1])
#
``` | instruction | 0 | 107,908 | 12 | 215,816 |
Yes | output | 1 | 107,908 | 12 | 215,817 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Recently, on the course of algorithms and data structures, Valeriy learned how to use a deque. He built a deque filled with n elements. The i-th element is a_i (i = 1, 2, …, n). He gradually takes the first two leftmost elements from the deque (let's call them A and B, respectively), and then does the following: if A > B, he writes A to the beginning and writes B to the end of the deque, otherwise, he writes to the beginning B, and A writes to the end of the deque. We call this sequence of actions an operation.
For example, if deque was [2, 3, 4, 5, 1], on the operation he will write B=3 to the beginning and A=2 to the end, so he will get [3, 4, 5, 1, 2].
The teacher of the course, seeing Valeriy, who was passionate about his work, approached him and gave him q queries. Each query consists of the singular number m_j (j = 1, 2, …, q). It is required for each query to answer which two elements he will pull out on the m_j-th operation.
Note that the queries are independent and for each query the numbers A and B should be printed in the order in which they will be pulled out of the deque.
Deque is a data structure representing a list of elements where insertion of new elements or deletion of existing elements can be made from both sides.
Input
The first line contains two integers n and q (2 ≤ n ≤ 10^5, 0 ≤ q ≤ 3 ⋅ 10^5) — the number of elements in the deque and the number of queries. The second line contains n integers a_1, a_2, ..., a_n, where a_i (0 ≤ a_i ≤ 10^9) — the deque element in i-th position. The next q lines contain one number each, meaning m_j (1 ≤ m_j ≤ 10^{18}).
Output
For each teacher's query, output two numbers A and B — the numbers that Valeriy pulls out of the deque for the m_j-th operation.
Examples
Input
5 3
1 2 3 4 5
1
2
10
Output
1 2
2 3
5 2
Input
2 0
0 0
Output
Note
Consider all 10 steps for the first test in detail:
1. [1, 2, 3, 4, 5] — on the first operation, A and B are 1 and 2, respectively.
So, 2 we write to the beginning of the deque, and 1 — to the end.
We get the following status of the deque: [2, 3, 4, 5, 1].
2. [2, 3, 4, 5, 1] ⇒ A = 2, B = 3.
3. [3, 4, 5, 1, 2]
4. [4, 5, 1, 2, 3]
5. [5, 1, 2, 3, 4]
6. [5, 2, 3, 4, 1]
7. [5, 3, 4, 1, 2]
8. [5, 4, 1, 2, 3]
9. [5, 1, 2, 3, 4]
10. [5, 2, 3, 4, 1] ⇒ A = 5, B = 2.
Submitted Solution:
```
n, q = map(int, input().split())
l = list(map(int, input().split()))
l2 = list()
first, second = l[0], l[1]
for i in range(1, n-1):
if first<=second:
l2.append(first)
first = second
else:
l2.append(second)
second = l[i+1]
if first<=second:
l2.append(first)
else:
l2.append(second)
maxx = max(l)
for _ in range(q):
m = int(input())
if 0<m<n:
first, second = l[0], l[1]
for i in range(1, m):
if first <= second:
first = second
second = l[i+1]
print(first, second)
else:
print(maxx, l2[m%(n-1)-1])
``` | instruction | 0 | 107,909 | 12 | 215,818 |
Yes | output | 1 | 107,909 | 12 | 215,819 |
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