message stringlengths 2 44.5k | message_type stringclasses 2
values | message_id int64 0 1 | conversation_id int64 42 109k | cluster float64 5 5 | __index_level_0__ int64 84 217k |
|---|---|---|---|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let us define the beauty of a sequence (a_1,... ,a_n) as the number of pairs of two adjacent elements in it whose absolute differences are d. For example, when d=1, the beauty of the sequence (3, 2, 3, 10, 9) is 3.
There are a total of n^m sequences of length m where each element is an integer between 1 and n (inclusive). Find the beauty of each of these n^m sequences, and print the average of those values.
Constraints
* 0 \leq d < n \leq 10^9
* 2 \leq m \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
n m d
Output
Print the average of the beauties of the sequences of length m where each element is an integer between 1 and n. The output will be judged correct if the absolute or relative error is at most 10^{-6}.
Examples
Input
2 3 1
Output
1.0000000000
Input
1000000000 180707 0
Output
0.0001807060
Submitted Solution:
```
import math
num_str=input().split()
num = list(map(int, num_str))
n = num[0]
m = num[1]
d = num[2]
num = math.pow(n, m)
score = 0
for i in range(1,m+1):
for j in range(1, n + 1):
for k in range(1, n + 1):
if abs(j - k) == d:
score += math.pow(n,m-i-1)
print(score/num)
``` | instruction | 0 | 26,324 | 5 | 52,648 |
No | output | 1 | 26,324 | 5 | 52,649 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The smallest unit of data handled by a computer is called a bit, and the amount of information that represents multiple bits together is called a word. Currently, many computers process one word as 32 bits.
For a computer that represents one word in 32 bits, create a program that outputs the amount of data W given in word units in bit units.
Input
The input is given in the following format.
W
The input consists of one line and is given the amount of data W (0 ≤ W ≤ 100).
Output
Outputs the bitwise value on one line.
Examples
Input
4
Output
128
Input
3
Output
96
Submitted Solution:
```
try:
while True:
i=int(input())
print(i*32)
except EOFError:
pass
``` | instruction | 0 | 26,424 | 5 | 52,848 |
No | output | 1 | 26,424 | 5 | 52,849 |
Provide a correct Python 3 solution for this coding contest problem.
> I would, if I could,
> If I couldn't how could I?
> I couldn't, without I could, could I?
> Could you, without you could, could ye?
> Could ye? could ye?
> Could you, without you could, could ye?
It is true, as this old rhyme says, that we can only DO what we can DO and we cannot DO what we cannot DO. Changing some of DOs with COUNTs, we have another statement that we can only COUNT what we can DO and we cannot COUNT what we cannot DO, which looks rather false. We could count what we could do as well as we could count what we couldn't do. Couldn't we, if we confine ourselves to finite issues?
Surely we can count, in principle, both what we can do and what we cannot do, if the object space is finite. Yet, sometimes we cannot count in practice what we can do or what we cannot do. Here, you are challenged, in a set of all positive integers up to (and including) a given bound n, to count all the integers that cannot be represented by a formula of the form a*i+b*j, where a and b are given positive integers and i and j are variables ranging over non-negative integers. You are requested to report only the result of the count, i.e. how many integers are not representable. For example, given n = 7, a = 2, b = 5, you should answer 2, since 1 and 3 cannot be represented in a specified form, and the other five numbers are representable as follows:
2 = 2*1 + 5*0, 4 = 2*2 + 5*0, 5 = 2*0 + 5*1,
6 = 2*3 + 5*0, 7 = 2*1 + 5*1.
Input
The input is a sequence of lines. Each line consists of three integers, n, a and b, in this order, separated by a space. The integers n, a and b are all positive and at most one million, except those in the last line. The last line consists of three zeros.
Output
For each input line except the last one, your program should write out a line that contains only the result of the count.
Example
Input
10 2 3
10 2 5
100 5 25
0 0 0
Output
1
2
80 | instruction | 0 | 26,435 | 5 | 52,870 |
"Correct Solution:
```
while 1:
n,a,b=map(int,input().split())
if n==a==b==0:break
c=0;d=[1]+[0]*1000000
for i in range(0,n+1):
if d[i]:
if i+a<=n:d[i+a]=1
if i+b<=n:d[i+b]=1
else:c+=1
print(c)
``` | output | 1 | 26,435 | 5 | 52,871 |
Provide a correct Python 3 solution for this coding contest problem.
> I would, if I could,
> If I couldn't how could I?
> I couldn't, without I could, could I?
> Could you, without you could, could ye?
> Could ye? could ye?
> Could you, without you could, could ye?
It is true, as this old rhyme says, that we can only DO what we can DO and we cannot DO what we cannot DO. Changing some of DOs with COUNTs, we have another statement that we can only COUNT what we can DO and we cannot COUNT what we cannot DO, which looks rather false. We could count what we could do as well as we could count what we couldn't do. Couldn't we, if we confine ourselves to finite issues?
Surely we can count, in principle, both what we can do and what we cannot do, if the object space is finite. Yet, sometimes we cannot count in practice what we can do or what we cannot do. Here, you are challenged, in a set of all positive integers up to (and including) a given bound n, to count all the integers that cannot be represented by a formula of the form a*i+b*j, where a and b are given positive integers and i and j are variables ranging over non-negative integers. You are requested to report only the result of the count, i.e. how many integers are not representable. For example, given n = 7, a = 2, b = 5, you should answer 2, since 1 and 3 cannot be represented in a specified form, and the other five numbers are representable as follows:
2 = 2*1 + 5*0, 4 = 2*2 + 5*0, 5 = 2*0 + 5*1,
6 = 2*3 + 5*0, 7 = 2*1 + 5*1.
Input
The input is a sequence of lines. Each line consists of three integers, n, a and b, in this order, separated by a space. The integers n, a and b are all positive and at most one million, except those in the last line. The last line consists of three zeros.
Output
For each input line except the last one, your program should write out a line that contains only the result of the count.
Example
Input
10 2 3
10 2 5
100 5 25
0 0 0
Output
1
2
80 | instruction | 0 | 26,436 | 5 | 52,872 |
"Correct Solution:
```
while 1:
n,a,b=map(int,input().split())
if n==a==b==0:break
c=0;d=[1]*(n+1)
for x in range(a):
for i in range(x*b,n+1,a):d[i]=0
print(sum(d))
``` | output | 1 | 26,436 | 5 | 52,873 |
Provide a correct Python 3 solution for this coding contest problem.
> I would, if I could,
> If I couldn't how could I?
> I couldn't, without I could, could I?
> Could you, without you could, could ye?
> Could ye? could ye?
> Could you, without you could, could ye?
It is true, as this old rhyme says, that we can only DO what we can DO and we cannot DO what we cannot DO. Changing some of DOs with COUNTs, we have another statement that we can only COUNT what we can DO and we cannot COUNT what we cannot DO, which looks rather false. We could count what we could do as well as we could count what we couldn't do. Couldn't we, if we confine ourselves to finite issues?
Surely we can count, in principle, both what we can do and what we cannot do, if the object space is finite. Yet, sometimes we cannot count in practice what we can do or what we cannot do. Here, you are challenged, in a set of all positive integers up to (and including) a given bound n, to count all the integers that cannot be represented by a formula of the form a*i+b*j, where a and b are given positive integers and i and j are variables ranging over non-negative integers. You are requested to report only the result of the count, i.e. how many integers are not representable. For example, given n = 7, a = 2, b = 5, you should answer 2, since 1 and 3 cannot be represented in a specified form, and the other five numbers are representable as follows:
2 = 2*1 + 5*0, 4 = 2*2 + 5*0, 5 = 2*0 + 5*1,
6 = 2*3 + 5*0, 7 = 2*1 + 5*1.
Input
The input is a sequence of lines. Each line consists of three integers, n, a and b, in this order, separated by a space. The integers n, a and b are all positive and at most one million, except those in the last line. The last line consists of three zeros.
Output
For each input line except the last one, your program should write out a line that contains only the result of the count.
Example
Input
10 2 3
10 2 5
100 5 25
0 0 0
Output
1
2
80 | instruction | 0 | 26,437 | 5 | 52,874 |
"Correct Solution:
```
while 1:
n,a,b=map(int,input().split())
if n==0:break
d=[1]*(n+1)
for x in range(a):
for i in range(x*b,n+1,a):d[i]=0
print(sum(d))
``` | output | 1 | 26,437 | 5 | 52,875 |
Provide a correct Python 3 solution for this coding contest problem.
> I would, if I could,
> If I couldn't how could I?
> I couldn't, without I could, could I?
> Could you, without you could, could ye?
> Could ye? could ye?
> Could you, without you could, could ye?
It is true, as this old rhyme says, that we can only DO what we can DO and we cannot DO what we cannot DO. Changing some of DOs with COUNTs, we have another statement that we can only COUNT what we can DO and we cannot COUNT what we cannot DO, which looks rather false. We could count what we could do as well as we could count what we couldn't do. Couldn't we, if we confine ourselves to finite issues?
Surely we can count, in principle, both what we can do and what we cannot do, if the object space is finite. Yet, sometimes we cannot count in practice what we can do or what we cannot do. Here, you are challenged, in a set of all positive integers up to (and including) a given bound n, to count all the integers that cannot be represented by a formula of the form a*i+b*j, where a and b are given positive integers and i and j are variables ranging over non-negative integers. You are requested to report only the result of the count, i.e. how many integers are not representable. For example, given n = 7, a = 2, b = 5, you should answer 2, since 1 and 3 cannot be represented in a specified form, and the other five numbers are representable as follows:
2 = 2*1 + 5*0, 4 = 2*2 + 5*0, 5 = 2*0 + 5*1,
6 = 2*3 + 5*0, 7 = 2*1 + 5*1.
Input
The input is a sequence of lines. Each line consists of three integers, n, a and b, in this order, separated by a space. The integers n, a and b are all positive and at most one million, except those in the last line. The last line consists of three zeros.
Output
For each input line except the last one, your program should write out a line that contains only the result of the count.
Example
Input
10 2 3
10 2 5
100 5 25
0 0 0
Output
1
2
80 | instruction | 0 | 26,438 | 5 | 52,876 |
"Correct Solution:
```
while True:
n,a,b = map(int, input().split())
if n==0: break
ok = [1]*(n+1)
for i in range(b):
for j in range(0,n-i*a+1,b):
ok[i*a+j] = 0
print(sum(ok))
``` | output | 1 | 26,438 | 5 | 52,877 |
Provide a correct Python 3 solution for this coding contest problem.
> I would, if I could,
> If I couldn't how could I?
> I couldn't, without I could, could I?
> Could you, without you could, could ye?
> Could ye? could ye?
> Could you, without you could, could ye?
It is true, as this old rhyme says, that we can only DO what we can DO and we cannot DO what we cannot DO. Changing some of DOs with COUNTs, we have another statement that we can only COUNT what we can DO and we cannot COUNT what we cannot DO, which looks rather false. We could count what we could do as well as we could count what we couldn't do. Couldn't we, if we confine ourselves to finite issues?
Surely we can count, in principle, both what we can do and what we cannot do, if the object space is finite. Yet, sometimes we cannot count in practice what we can do or what we cannot do. Here, you are challenged, in a set of all positive integers up to (and including) a given bound n, to count all the integers that cannot be represented by a formula of the form a*i+b*j, where a and b are given positive integers and i and j are variables ranging over non-negative integers. You are requested to report only the result of the count, i.e. how many integers are not representable. For example, given n = 7, a = 2, b = 5, you should answer 2, since 1 and 3 cannot be represented in a specified form, and the other five numbers are representable as follows:
2 = 2*1 + 5*0, 4 = 2*2 + 5*0, 5 = 2*0 + 5*1,
6 = 2*3 + 5*0, 7 = 2*1 + 5*1.
Input
The input is a sequence of lines. Each line consists of three integers, n, a and b, in this order, separated by a space. The integers n, a and b are all positive and at most one million, except those in the last line. The last line consists of three zeros.
Output
For each input line except the last one, your program should write out a line that contains only the result of the count.
Example
Input
10 2 3
10 2 5
100 5 25
0 0 0
Output
1
2
80 | instruction | 0 | 26,439 | 5 | 52,878 |
"Correct Solution:
```
while 1:
n,a,b=map(int,input().split())
if n==a==b==0:break
c=0;d=[1]+[0]*2000000
for i in range(0,n+1):
if d[i]:d[i+a]=d[i+b]=1
else:c+=1
print(c)
``` | output | 1 | 26,439 | 5 | 52,879 |
Provide a correct Python 3 solution for this coding contest problem.
> I would, if I could,
> If I couldn't how could I?
> I couldn't, without I could, could I?
> Could you, without you could, could ye?
> Could ye? could ye?
> Could you, without you could, could ye?
It is true, as this old rhyme says, that we can only DO what we can DO and we cannot DO what we cannot DO. Changing some of DOs with COUNTs, we have another statement that we can only COUNT what we can DO and we cannot COUNT what we cannot DO, which looks rather false. We could count what we could do as well as we could count what we couldn't do. Couldn't we, if we confine ourselves to finite issues?
Surely we can count, in principle, both what we can do and what we cannot do, if the object space is finite. Yet, sometimes we cannot count in practice what we can do or what we cannot do. Here, you are challenged, in a set of all positive integers up to (and including) a given bound n, to count all the integers that cannot be represented by a formula of the form a*i+b*j, where a and b are given positive integers and i and j are variables ranging over non-negative integers. You are requested to report only the result of the count, i.e. how many integers are not representable. For example, given n = 7, a = 2, b = 5, you should answer 2, since 1 and 3 cannot be represented in a specified form, and the other five numbers are representable as follows:
2 = 2*1 + 5*0, 4 = 2*2 + 5*0, 5 = 2*0 + 5*1,
6 = 2*3 + 5*0, 7 = 2*1 + 5*1.
Input
The input is a sequence of lines. Each line consists of three integers, n, a and b, in this order, separated by a space. The integers n, a and b are all positive and at most one million, except those in the last line. The last line consists of three zeros.
Output
For each input line except the last one, your program should write out a line that contains only the result of the count.
Example
Input
10 2 3
10 2 5
100 5 25
0 0 0
Output
1
2
80 | instruction | 0 | 26,440 | 5 | 52,880 |
"Correct Solution:
```
while True:
n, a, b = map(int, input().split())
if not n:
break
if a > b:
a, b = b, a
dp = [False] * (n + b - a + 1)
dp[1:n + 1] = [True] * n
for i in range(n - a + 1):
if not dp[i]:
dp[i + a] = False
dp[i + b] = False
print(dp.count(True))
``` | output | 1 | 26,440 | 5 | 52,881 |
Provide a correct Python 3 solution for this coding contest problem.
> I would, if I could,
> If I couldn't how could I?
> I couldn't, without I could, could I?
> Could you, without you could, could ye?
> Could ye? could ye?
> Could you, without you could, could ye?
It is true, as this old rhyme says, that we can only DO what we can DO and we cannot DO what we cannot DO. Changing some of DOs with COUNTs, we have another statement that we can only COUNT what we can DO and we cannot COUNT what we cannot DO, which looks rather false. We could count what we could do as well as we could count what we couldn't do. Couldn't we, if we confine ourselves to finite issues?
Surely we can count, in principle, both what we can do and what we cannot do, if the object space is finite. Yet, sometimes we cannot count in practice what we can do or what we cannot do. Here, you are challenged, in a set of all positive integers up to (and including) a given bound n, to count all the integers that cannot be represented by a formula of the form a*i+b*j, where a and b are given positive integers and i and j are variables ranging over non-negative integers. You are requested to report only the result of the count, i.e. how many integers are not representable. For example, given n = 7, a = 2, b = 5, you should answer 2, since 1 and 3 cannot be represented in a specified form, and the other five numbers are representable as follows:
2 = 2*1 + 5*0, 4 = 2*2 + 5*0, 5 = 2*0 + 5*1,
6 = 2*3 + 5*0, 7 = 2*1 + 5*1.
Input
The input is a sequence of lines. Each line consists of three integers, n, a and b, in this order, separated by a space. The integers n, a and b are all positive and at most one million, except those in the last line. The last line consists of three zeros.
Output
For each input line except the last one, your program should write out a line that contains only the result of the count.
Example
Input
10 2 3
10 2 5
100 5 25
0 0 0
Output
1
2
80 | instruction | 0 | 26,441 | 5 | 52,882 |
"Correct Solution:
```
# AOJ 1105: Unable Count
# Python3 2018.7.14 bal4u
while True:
n, a, b = map(int, input().split())
if n == 0: break
f = [0]*(n+max(a,b)+1)
f[0], f[a], f[b] = 1, 1, 1
s = min(a, b)
for k in range(s, n+1):
if f[k]: f[a+k] = 1; f[b+k] = 1
print(n-sum(f[s:n+1]))
``` | output | 1 | 26,441 | 5 | 52,883 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
> I would, if I could,
> If I couldn't how could I?
> I couldn't, without I could, could I?
> Could you, without you could, could ye?
> Could ye? could ye?
> Could you, without you could, could ye?
It is true, as this old rhyme says, that we can only DO what we can DO and we cannot DO what we cannot DO. Changing some of DOs with COUNTs, we have another statement that we can only COUNT what we can DO and we cannot COUNT what we cannot DO, which looks rather false. We could count what we could do as well as we could count what we couldn't do. Couldn't we, if we confine ourselves to finite issues?
Surely we can count, in principle, both what we can do and what we cannot do, if the object space is finite. Yet, sometimes we cannot count in practice what we can do or what we cannot do. Here, you are challenged, in a set of all positive integers up to (and including) a given bound n, to count all the integers that cannot be represented by a formula of the form a*i+b*j, where a and b are given positive integers and i and j are variables ranging over non-negative integers. You are requested to report only the result of the count, i.e. how many integers are not representable. For example, given n = 7, a = 2, b = 5, you should answer 2, since 1 and 3 cannot be represented in a specified form, and the other five numbers are representable as follows:
2 = 2*1 + 5*0, 4 = 2*2 + 5*0, 5 = 2*0 + 5*1,
6 = 2*3 + 5*0, 7 = 2*1 + 5*1.
Input
The input is a sequence of lines. Each line consists of three integers, n, a and b, in this order, separated by a space. The integers n, a and b are all positive and at most one million, except those in the last line. The last line consists of three zeros.
Output
For each input line except the last one, your program should write out a line that contains only the result of the count.
Example
Input
10 2 3
10 2 5
100 5 25
0 0 0
Output
1
2
80
Submitted Solution:
```
while True:
n, a, b = map(int, input().split())
if not n:
break
dp = [False] * (n + abs(a - b))
dp[1:n + 1] = [True] * n
for i in range(n - min(a, b)):
if not dp[i]:
dp[i + a] = False
dp[i + b] = False
print(dp.count(True))
``` | instruction | 0 | 26,442 | 5 | 52,884 |
No | output | 1 | 26,442 | 5 | 52,885 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
> I would, if I could,
> If I couldn't how could I?
> I couldn't, without I could, could I?
> Could you, without you could, could ye?
> Could ye? could ye?
> Could you, without you could, could ye?
It is true, as this old rhyme says, that we can only DO what we can DO and we cannot DO what we cannot DO. Changing some of DOs with COUNTs, we have another statement that we can only COUNT what we can DO and we cannot COUNT what we cannot DO, which looks rather false. We could count what we could do as well as we could count what we couldn't do. Couldn't we, if we confine ourselves to finite issues?
Surely we can count, in principle, both what we can do and what we cannot do, if the object space is finite. Yet, sometimes we cannot count in practice what we can do or what we cannot do. Here, you are challenged, in a set of all positive integers up to (and including) a given bound n, to count all the integers that cannot be represented by a formula of the form a*i+b*j, where a and b are given positive integers and i and j are variables ranging over non-negative integers. You are requested to report only the result of the count, i.e. how many integers are not representable. For example, given n = 7, a = 2, b = 5, you should answer 2, since 1 and 3 cannot be represented in a specified form, and the other five numbers are representable as follows:
2 = 2*1 + 5*0, 4 = 2*2 + 5*0, 5 = 2*0 + 5*1,
6 = 2*3 + 5*0, 7 = 2*1 + 5*1.
Input
The input is a sequence of lines. Each line consists of three integers, n, a and b, in this order, separated by a space. The integers n, a and b are all positive and at most one million, except those in the last line. The last line consists of three zeros.
Output
For each input line except the last one, your program should write out a line that contains only the result of the count.
Example
Input
10 2 3
10 2 5
100 5 25
0 0 0
Output
1
2
80
Submitted Solution:
```
# AOJ 1105: Unable Count
# Python3 2018.7.14 bal4u
while True:
n, a, b = map(int, input().split())
if n == 0: break
f = [0]*(n>>1)
for x in range(0, n, a):
for y in range(0, n+1, b): f[x+y] = 1
print(n-sum(f[1:n+1]))
``` | instruction | 0 | 26,443 | 5 | 52,886 |
No | output | 1 | 26,443 | 5 | 52,887 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
> I would, if I could,
> If I couldn't how could I?
> I couldn't, without I could, could I?
> Could you, without you could, could ye?
> Could ye? could ye?
> Could you, without you could, could ye?
It is true, as this old rhyme says, that we can only DO what we can DO and we cannot DO what we cannot DO. Changing some of DOs with COUNTs, we have another statement that we can only COUNT what we can DO and we cannot COUNT what we cannot DO, which looks rather false. We could count what we could do as well as we could count what we couldn't do. Couldn't we, if we confine ourselves to finite issues?
Surely we can count, in principle, both what we can do and what we cannot do, if the object space is finite. Yet, sometimes we cannot count in practice what we can do or what we cannot do. Here, you are challenged, in a set of all positive integers up to (and including) a given bound n, to count all the integers that cannot be represented by a formula of the form a*i+b*j, where a and b are given positive integers and i and j are variables ranging over non-negative integers. You are requested to report only the result of the count, i.e. how many integers are not representable. For example, given n = 7, a = 2, b = 5, you should answer 2, since 1 and 3 cannot be represented in a specified form, and the other five numbers are representable as follows:
2 = 2*1 + 5*0, 4 = 2*2 + 5*0, 5 = 2*0 + 5*1,
6 = 2*3 + 5*0, 7 = 2*1 + 5*1.
Input
The input is a sequence of lines. Each line consists of three integers, n, a and b, in this order, separated by a space. The integers n, a and b are all positive and at most one million, except those in the last line. The last line consists of three zeros.
Output
For each input line except the last one, your program should write out a line that contains only the result of the count.
Example
Input
10 2 3
10 2 5
100 5 25
0 0 0
Output
1
2
80
Submitted Solution:
```
# AOJ 1105: Unable Count
# Python3 2018.7.14 bal4u
while True:
n, a, b = map(int, input().split())
if n == 0: break
f = [0]*(n<<1)
for x in range(0, n, a):
for y in range(0, n+1, b): f[x+y] = 1
print(n-sum(f[1:n+1]))
``` | instruction | 0 | 26,444 | 5 | 52,888 |
No | output | 1 | 26,444 | 5 | 52,889 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
> I would, if I could,
> If I couldn't how could I?
> I couldn't, without I could, could I?
> Could you, without you could, could ye?
> Could ye? could ye?
> Could you, without you could, could ye?
It is true, as this old rhyme says, that we can only DO what we can DO and we cannot DO what we cannot DO. Changing some of DOs with COUNTs, we have another statement that we can only COUNT what we can DO and we cannot COUNT what we cannot DO, which looks rather false. We could count what we could do as well as we could count what we couldn't do. Couldn't we, if we confine ourselves to finite issues?
Surely we can count, in principle, both what we can do and what we cannot do, if the object space is finite. Yet, sometimes we cannot count in practice what we can do or what we cannot do. Here, you are challenged, in a set of all positive integers up to (and including) a given bound n, to count all the integers that cannot be represented by a formula of the form a*i+b*j, where a and b are given positive integers and i and j are variables ranging over non-negative integers. You are requested to report only the result of the count, i.e. how many integers are not representable. For example, given n = 7, a = 2, b = 5, you should answer 2, since 1 and 3 cannot be represented in a specified form, and the other five numbers are representable as follows:
2 = 2*1 + 5*0, 4 = 2*2 + 5*0, 5 = 2*0 + 5*1,
6 = 2*3 + 5*0, 7 = 2*1 + 5*1.
Input
The input is a sequence of lines. Each line consists of three integers, n, a and b, in this order, separated by a space. The integers n, a and b are all positive and at most one million, except those in the last line. The last line consists of three zeros.
Output
For each input line except the last one, your program should write out a line that contains only the result of the count.
Example
Input
10 2 3
10 2 5
100 5 25
0 0 0
Output
1
2
80
Submitted Solution:
```
# AOJ 1105: Unable Count
# Python3 2018.7.14 bal4u
while True:
n, a, b = map(int, input().split())
if n == 0: break
f = [0]*(n+1)
for x in range(0, n, a):
for y in range(0, n+1, b): f[x+y] = 1
print(n-sum(f))
``` | instruction | 0 | 26,445 | 5 | 52,890 |
No | output | 1 | 26,445 | 5 | 52,891 |
Provide a correct Python 3 solution for this coding contest problem.
The ACM ICPC judges are very careful about not leaking their problems, and all communications are encrypted. However, one does sometimes make mistakes, like using too weak an encryption scheme. Here is an example of that.
The encryption chosen was very simple: encrypt each chunk of the input by flipping some bits according to a shared key. To provide reasonable security, the size of both chunk and key is 32 bits.
That is, suppose the input was a sequence of m 32-bit integers.
N1 N2 N3 ... Nm
After encoding with the key K it becomes the following sequence of m 32-bit integers.
(N1 ∧ K) (N2 ∧ K) (N3 ∧ K) ... (Nm ∧ K)
where (a ∧ b) is the bitwise exclusive or of a and b.
Exclusive or is the logical operator which is 1 when only one of its operands is 1, and 0 otherwise. Here is its definition for 1-bit integers.
0 ⊕ 0 = 0 0 ⊕ 1 = 1
1 ⊕ 0 = 1 1 ⊕ 1 =0
As you can see, it is identical to addition modulo 2. For two 32-bit integers a and b, their bitwise exclusive or a ∧ b is defined as follows, using their binary representations, composed of 0's and 1's.
a ∧ b = a31 ... a1a0 ∧ b31 ... b1b0 = c31 ... c1c0
where
ci = ai ⊕ bi (i = 0, 1, ... , 31).
For instance, using binary notation, 11010110 ∧ 01010101 = 10100011, or using hexadecimal,
d6 ∧ 55 = a3.
Since this kind of encryption is notoriously weak to statistical attacks, the message has to be compressed in advance, so that it has no statistical regularity. We suppose that N1 N2 ... Nm is already in compressed form.
However, the trouble is that the compression algorithm itself introduces some form of regularity: after every 8 integers of compressed data, it inserts a checksum, the sum of these integers. That is, in the above input, N9 = ∑8i=1 Ni = N1 + ... + N8, where additions are modulo 232.
Luckily, you could intercept a communication between the judges. Maybe it contains a problem for the finals!
As you are very clever, you have certainly seen that you can easily find the lowest bit of the key, denoted by K0. On the one hand, if K0 = 1, then after encoding, the lowest bit of ∑8i=1 Ni ∧ K is unchanged, as K0 is added an even number of times, but the lowest bit of N9 ∧ K is changed, so they shall differ. On the other hand, if K0 = 0, then after encoding, the lowest bit of ∑8i=1 Ni ∧ K shall still be identical to the lowest bit of N9 ∧ K, as they do not change. For instance, if the lowest bits after encoding are 1 1 1 1 1 1 1 1 1 then K0 must be 1, but if they are 1 1 1 1 1 1 1 0 1 then K0 must be 0.
So far, so good. Can you do better?
You should find the key used for encoding.
Input
The input starts with a line containing only a positive integer S, indicating the number of datasets in the input. S is no more than 1000.
It is followed by S datasets. Each dataset is composed of nine 32-bit integers corresponding to the first nine chunks of a communication. They are written in hexadecimal notation, using digits ‘0’ to ‘9’ and lowercase letters ‘a’ to ‘f’, and with no leading zeros. They are separated by a space or a newline. Each dataset is ended by a newline.
Output
For each dataset you should output the key used for encoding. Each key shall appear alone on its line, and be written in hexadecimal notation, using digits ‘0’ to ‘9’ and lowercase letters ‘a’ to ‘f’, and with no leading zeros.
Example
Input
8
1 1 1 1 1 1 1 1 8
3 2 3 2 3 2 3 2 6
3 4 4 7 7 b a 2 2e
e1 13 ce 28 ca 6 ab 46 a6d
b08 49e2 6128 f27 8cf2 bc50 7380 7fe1 723b
4eba eb4 a352 fd14 6ac1 eed1 dd06 bb83 392bc
ef593c08 847e522f 74c02b9c 26f3a4e1 e2720a01 6fe66007
7a4e96ad 6ee5cef6 3853cd88
60202fb8 757d6d66 9c3a9525 fbcd7983 82b9571c ddc54bab 853e52da
22047c88 e5524401
Output
0
2
6
1c6
4924afc7
ffff95c5
546991d
901c4a16 | instruction | 0 | 26,446 | 5 | 52,892 |
"Correct Solution:
```
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools
sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**10
mod = 998244353
dd = [(0,-1),(1,0),(0,1),(-1,0)]
ddn = [(0,-1),(1,-1),(1,0),(1,1),(0,1),(-1,-1),(-1,0),(-1,1)]
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)
def main():
rr = []
n = I()
ni = 0
while ni < n:
ni += 1
a = []
while len(a) < 9:
a += LS()
t = int(a[-1],16)
a = list(map(lambda x: int(x,16), a[:-1]))
r = 0
for i in range(32):
ii = 2**i
iii = 2**(i+1)
b = t & ii
c = 0
for d in a:
c += d^r
if (c & ii) != b:
r += ii
rr.append('{:0x}'.format(r))
return '\n'.join(map(str, rr))
print(main())
``` | output | 1 | 26,446 | 5 | 52,893 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a sequence of n integers S and a sequence of different q integers T. Write a program which outputs C, the number of integers in T which are also in the set S.
Notes
Constraints
* Elements in S is sorted in ascending order
* n ≤ 100000
* q ≤ 50000
* 0 ≤ an element in S ≤ 109
* 0 ≤ an element in T ≤ 109
Input
In the first line n is given. In the second line, n integers are given. In the third line q is given. Then, in the fourth line, q integers are given.
Output
Print C in a line.
Examples
Input
5
1 2 3 4 5
3
3 4 1
Output
3
Input
3
1 2 3
1
5
Output
0
Input
5
1 1 2 2 3
2
1 2
Output
2 | instruction | 0 | 26,522 | 5 | 53,044 |
"Correct Solution:
```
import sys
s=sys.stdin.readlines()
print(len(set(s[1].split())&set(s[3].split())))
``` | output | 1 | 26,522 | 5 | 53,045 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a sequence of n integers S and a sequence of different q integers T. Write a program which outputs C, the number of integers in T which are also in the set S.
Notes
Constraints
* Elements in S is sorted in ascending order
* n ≤ 100000
* q ≤ 50000
* 0 ≤ an element in S ≤ 109
* 0 ≤ an element in T ≤ 109
Input
In the first line n is given. In the second line, n integers are given. In the third line q is given. Then, in the fourth line, q integers are given.
Output
Print C in a line.
Examples
Input
5
1 2 3 4 5
3
3 4 1
Output
3
Input
3
1 2 3
1
5
Output
0
Input
5
1 1 2 2 3
2
1 2
Output
2 | instruction | 0 | 26,523 | 5 | 53,046 |
"Correct Solution:
```
n = int(input())
s = set(map(int, input().split()))
q = int(input())
t = set(map(int, input().split()))
print(len(s & t))
``` | output | 1 | 26,523 | 5 | 53,047 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a sequence of n integers S and a sequence of different q integers T. Write a program which outputs C, the number of integers in T which are also in the set S.
Notes
Constraints
* Elements in S is sorted in ascending order
* n ≤ 100000
* q ≤ 50000
* 0 ≤ an element in S ≤ 109
* 0 ≤ an element in T ≤ 109
Input
In the first line n is given. In the second line, n integers are given. In the third line q is given. Then, in the fourth line, q integers are given.
Output
Print C in a line.
Examples
Input
5
1 2 3 4 5
3
3 4 1
Output
3
Input
3
1 2 3
1
5
Output
0
Input
5
1 1 2 2 3
2
1 2
Output
2 | instruction | 0 | 26,524 | 5 | 53,048 |
"Correct Solution:
```
n1 = int(input())
s1 = set(map(int, input().strip().split()))
n2 = int(input())
s2 = set(map(int, input().strip().split()))
print(len(s1 & s2))
``` | output | 1 | 26,524 | 5 | 53,049 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a sequence of n integers S and a sequence of different q integers T. Write a program which outputs C, the number of integers in T which are also in the set S.
Notes
Constraints
* Elements in S is sorted in ascending order
* n ≤ 100000
* q ≤ 50000
* 0 ≤ an element in S ≤ 109
* 0 ≤ an element in T ≤ 109
Input
In the first line n is given. In the second line, n integers are given. In the third line q is given. Then, in the fourth line, q integers are given.
Output
Print C in a line.
Examples
Input
5
1 2 3 4 5
3
3 4 1
Output
3
Input
3
1 2 3
1
5
Output
0
Input
5
1 1 2 2 3
2
1 2
Output
2 | instruction | 0 | 26,525 | 5 | 53,050 |
"Correct Solution:
```
from collections import Counter
def main():
N = int(input())
S = tuple(map(int, input().split()))
Q = int(input())
T = tuple(map(int, input().split()))
counter = Counter(S)
cnt = 0
for i in T:
cnt += any([counter[i]])
print(cnt)
main()
``` | output | 1 | 26,525 | 5 | 53,051 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a sequence of n integers S and a sequence of different q integers T. Write a program which outputs C, the number of integers in T which are also in the set S.
Notes
Constraints
* Elements in S is sorted in ascending order
* n ≤ 100000
* q ≤ 50000
* 0 ≤ an element in S ≤ 109
* 0 ≤ an element in T ≤ 109
Input
In the first line n is given. In the second line, n integers are given. In the third line q is given. Then, in the fourth line, q integers are given.
Output
Print C in a line.
Examples
Input
5
1 2 3 4 5
3
3 4 1
Output
3
Input
3
1 2 3
1
5
Output
0
Input
5
1 1 2 2 3
2
1 2
Output
2 | instruction | 0 | 26,526 | 5 | 53,052 |
"Correct Solution:
```
import bisect
n = int(input())
S = list(map(int, input().split()))
q = int(input())
T = list(map(int, input().split()))
ans = 0
for i in T:
insert_index = bisect.bisect_left(S, i)
if insert_index == n:
continue
else:
if S[insert_index] == i:
ans += 1
print(ans)
``` | output | 1 | 26,526 | 5 | 53,053 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a sequence of n integers S and a sequence of different q integers T. Write a program which outputs C, the number of integers in T which are also in the set S.
Notes
Constraints
* Elements in S is sorted in ascending order
* n ≤ 100000
* q ≤ 50000
* 0 ≤ an element in S ≤ 109
* 0 ≤ an element in T ≤ 109
Input
In the first line n is given. In the second line, n integers are given. In the third line q is given. Then, in the fourth line, q integers are given.
Output
Print C in a line.
Examples
Input
5
1 2 3 4 5
3
3 4 1
Output
3
Input
3
1 2 3
1
5
Output
0
Input
5
1 1 2 2 3
2
1 2
Output
2 | instruction | 0 | 26,527 | 5 | 53,054 |
"Correct Solution:
```
from bisect import bisect_left
n = int(input())
S = list(map(int, input().split()))
p = int(input())
T = list(map(int, input().split()))
ans = 0
def sh(num):
ind = bisect_left(S, num)
return S[ind] == num
for t in T:
if sh(t):
ans += 1
print(ans)
``` | output | 1 | 26,527 | 5 | 53,055 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a sequence of n integers S and a sequence of different q integers T. Write a program which outputs C, the number of integers in T which are also in the set S.
Notes
Constraints
* Elements in S is sorted in ascending order
* n ≤ 100000
* q ≤ 50000
* 0 ≤ an element in S ≤ 109
* 0 ≤ an element in T ≤ 109
Input
In the first line n is given. In the second line, n integers are given. In the third line q is given. Then, in the fourth line, q integers are given.
Output
Print C in a line.
Examples
Input
5
1 2 3 4 5
3
3 4 1
Output
3
Input
3
1 2 3
1
5
Output
0
Input
5
1 1 2 2 3
2
1 2
Output
2 | instruction | 0 | 26,528 | 5 | 53,056 |
"Correct Solution:
```
s = int(input())
S = list(map(int, input().split()))
t= int(input())
T = list(map(int, input().split()))
cnt = 0
for i in T:
a=0
b=s-1
while b >= a:
mid=int((a+b)/2)
if S[mid]==i:
cnt+= 1
break
elif S[mid]>i:
b=mid-1
continue
else:
a=mid+1
continue
print(cnt)
``` | output | 1 | 26,528 | 5 | 53,057 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a sequence of n integers S and a sequence of different q integers T. Write a program which outputs C, the number of integers in T which are also in the set S.
Notes
Constraints
* Elements in S is sorted in ascending order
* n ≤ 100000
* q ≤ 50000
* 0 ≤ an element in S ≤ 109
* 0 ≤ an element in T ≤ 109
Input
In the first line n is given. In the second line, n integers are given. In the third line q is given. Then, in the fourth line, q integers are given.
Output
Print C in a line.
Examples
Input
5
1 2 3 4 5
3
3 4 1
Output
3
Input
3
1 2 3
1
5
Output
0
Input
5
1 1 2 2 3
2
1 2
Output
2 | instruction | 0 | 26,529 | 5 | 53,058 |
"Correct Solution:
```
input()
s = set(n for n in input().split())
input()
t = set(n for n in input().split())
print(len(s & t))
``` | output | 1 | 26,529 | 5 | 53,059 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a sequence of n integers S and a sequence of different q integers T. Write a program which outputs C, the number of integers in T which are also in the set S.
Notes
Constraints
* Elements in S is sorted in ascending order
* n ≤ 100000
* q ≤ 50000
* 0 ≤ an element in S ≤ 109
* 0 ≤ an element in T ≤ 109
Input
In the first line n is given. In the second line, n integers are given. In the third line q is given. Then, in the fourth line, q integers are given.
Output
Print C in a line.
Examples
Input
5
1 2 3 4 5
3
3 4 1
Output
3
Input
3
1 2 3
1
5
Output
0
Input
5
1 1 2 2 3
2
1 2
Output
2
Submitted Solution:
```
import collections
if __name__ == "__main__":
S_num = int(input())
S = collections.Counter(set(map(lambda x: int(x), input().split())))
T_num = int(input())
T = list(map(lambda x: int(x), input().split()))
print(f"{sum(map(lambda x: S[x], T))}")
``` | instruction | 0 | 26,530 | 5 | 53,060 |
Yes | output | 1 | 26,530 | 5 | 53,061 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a sequence of n integers S and a sequence of different q integers T. Write a program which outputs C, the number of integers in T which are also in the set S.
Notes
Constraints
* Elements in S is sorted in ascending order
* n ≤ 100000
* q ≤ 50000
* 0 ≤ an element in S ≤ 109
* 0 ≤ an element in T ≤ 109
Input
In the first line n is given. In the second line, n integers are given. In the third line q is given. Then, in the fourth line, q integers are given.
Output
Print C in a line.
Examples
Input
5
1 2 3 4 5
3
3 4 1
Output
3
Input
3
1 2 3
1
5
Output
0
Input
5
1 1 2 2 3
2
1 2
Output
2
Submitted Solution:
```
from bisect import bisect_left
n = int(input())
S = list(map(int, input().split()))
q = int(input())
T = list(map(int, input().split()))
S.sort()
ans = 0
for t in T:
i = bisect_left(S, t)
if 0<=i<n and S[i]==t:
ans += 1
print(ans)
``` | instruction | 0 | 26,531 | 5 | 53,062 |
Yes | output | 1 | 26,531 | 5 | 53,063 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a sequence of n integers S and a sequence of different q integers T. Write a program which outputs C, the number of integers in T which are also in the set S.
Notes
Constraints
* Elements in S is sorted in ascending order
* n ≤ 100000
* q ≤ 50000
* 0 ≤ an element in S ≤ 109
* 0 ≤ an element in T ≤ 109
Input
In the first line n is given. In the second line, n integers are given. In the third line q is given. Then, in the fourth line, q integers are given.
Output
Print C in a line.
Examples
Input
5
1 2 3 4 5
3
3 4 1
Output
3
Input
3
1 2 3
1
5
Output
0
Input
5
1 1 2 2 3
2
1 2
Output
2
Submitted Solution:
```
from bisect import bisect_left
n = int(input())
S = [int(i) for i in input().split()]
q = int(input())
T = [int(i) for i in input().split()]
count = 0
for t in T:
index = bisect_left(S, t)
if index < len(S) and S[index] == t:
count += 1
print(count)
``` | instruction | 0 | 26,532 | 5 | 53,064 |
Yes | output | 1 | 26,532 | 5 | 53,065 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a sequence of n integers S and a sequence of different q integers T. Write a program which outputs C, the number of integers in T which are also in the set S.
Notes
Constraints
* Elements in S is sorted in ascending order
* n ≤ 100000
* q ≤ 50000
* 0 ≤ an element in S ≤ 109
* 0 ≤ an element in T ≤ 109
Input
In the first line n is given. In the second line, n integers are given. In the third line q is given. Then, in the fourth line, q integers are given.
Output
Print C in a line.
Examples
Input
5
1 2 3 4 5
3
3 4 1
Output
3
Input
3
1 2 3
1
5
Output
0
Input
5
1 1 2 2 3
2
1 2
Output
2
Submitted Solution:
```
import bisect
n = int(input())
s = list(map(int, input().split()))
q = int(input())
t = list(map(int, input().split()))
cnt = 0
for i in t:
if s[bisect.bisect_left(s, i)] == i:
cnt += 1
print(cnt)
``` | instruction | 0 | 26,533 | 5 | 53,066 |
Yes | output | 1 | 26,533 | 5 | 53,067 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a sequence of n integers S and a sequence of different q integers T. Write a program which outputs C, the number of integers in T which are also in the set S.
Notes
Constraints
* Elements in S is sorted in ascending order
* n ≤ 100000
* q ≤ 50000
* 0 ≤ an element in S ≤ 109
* 0 ≤ an element in T ≤ 109
Input
In the first line n is given. In the second line, n integers are given. In the third line q is given. Then, in the fourth line, q integers are given.
Output
Print C in a line.
Examples
Input
5
1 2 3 4 5
3
3 4 1
Output
3
Input
3
1 2 3
1
5
Output
0
Input
5
1 1 2 2 3
2
1 2
Output
2
Submitted Solution:
```
c=0
n=int(input())
s=input().split()
q=int(input())
t=input().split()
l=list(set(s))
l.sort()
h=0
for i in t:
for j in l:
if int(i)==int(j) and h==int(i):
c +=1
h=j
break
print(c)
``` | instruction | 0 | 26,534 | 5 | 53,068 |
No | output | 1 | 26,534 | 5 | 53,069 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a sequence of n integers S and a sequence of different q integers T. Write a program which outputs C, the number of integers in T which are also in the set S.
Notes
Constraints
* Elements in S is sorted in ascending order
* n ≤ 100000
* q ≤ 50000
* 0 ≤ an element in S ≤ 109
* 0 ≤ an element in T ≤ 109
Input
In the first line n is given. In the second line, n integers are given. In the third line q is given. Then, in the fourth line, q integers are given.
Output
Print C in a line.
Examples
Input
5
1 2 3 4 5
3
3 4 1
Output
3
Input
3
1 2 3
1
5
Output
0
Input
5
1 1 2 2 3
2
1 2
Output
2
Submitted Solution:
```
#16D8103010K Ko Okasaki
#ALDS4_B
n=int(input())
Q=input.split()
q=int(input())
S=input.split()
Q=list(map(int,Q))
S=list(map(int,S))
cnt=1
for i in range(q):
left=0
right=n-1
while left<=right:
mid=int((n-1)/2)
if S[mid]==Q[i]:
cnt+=1
break
elif S[mid]>Q[i]:
right=mid
elif S[mid]<Q[i]:
left=mid
print(cnt)
``` | instruction | 0 | 26,535 | 5 | 53,070 |
No | output | 1 | 26,535 | 5 | 53,071 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a sequence of n integers S and a sequence of different q integers T. Write a program which outputs C, the number of integers in T which are also in the set S.
Notes
Constraints
* Elements in S is sorted in ascending order
* n ≤ 100000
* q ≤ 50000
* 0 ≤ an element in S ≤ 109
* 0 ≤ an element in T ≤ 109
Input
In the first line n is given. In the second line, n integers are given. In the third line q is given. Then, in the fourth line, q integers are given.
Output
Print C in a line.
Examples
Input
5
1 2 3 4 5
3
3 4 1
Output
3
Input
3
1 2 3
1
5
Output
0
Input
5
1 1 2 2 3
2
1 2
Output
2
Submitted Solution:
```
def binarysearch(ary, num):
if len(ary) == 1 and ary[0] != num: return -1
mid = len(ary) // 2
if num < ary[mid]:
return binarysearch(ary[:mid], num)
elif num > ary[mid]:
return binarysearch(ary[mid+1:], num)
else:
return ary[mid]
n = int(input())
s = list(map(lambda i: int(i), input().split(" ")))
q = int(input())
t = list(map(lambda i: int(i), input().split(" ")))
c = 0
for i in t:
if binarysearch(s, i) != -1: c += 1
print(c)
``` | instruction | 0 | 26,536 | 5 | 53,072 |
No | output | 1 | 26,536 | 5 | 53,073 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a sequence of n integers S and a sequence of different q integers T. Write a program which outputs C, the number of integers in T which are also in the set S.
Notes
Constraints
* Elements in S is sorted in ascending order
* n ≤ 100000
* q ≤ 50000
* 0 ≤ an element in S ≤ 109
* 0 ≤ an element in T ≤ 109
Input
In the first line n is given. In the second line, n integers are given. In the third line q is given. Then, in the fourth line, q integers are given.
Output
Print C in a line.
Examples
Input
5
1 2 3 4 5
3
3 4 1
Output
3
Input
3
1 2 3
1
5
Output
0
Input
5
1 1 2 2 3
2
1 2
Output
2
Submitted Solution:
```
n = int(input())
S = list(map(int, input().split()))
q = int(input())
T = list(map(int, input().split()))
Sum = 0
for i in T:
if i in S:
Sum += 1
print(Sum)
``` | instruction | 0 | 26,537 | 5 | 53,074 |
No | output | 1 | 26,537 | 5 | 53,075 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
It is the hard version of the problem. The only difference is that in this version 3 ≤ k ≤ n.
You are given a positive integer n. Find k positive integers a_1, a_2, …, a_k, such that:
* a_1 + a_2 + … + a_k = n
* LCM(a_1, a_2, …, a_k) ≤ n/2
Here LCM is the [least common multiple](https://en.wikipedia.org/wiki/Least_common_multiple) of numbers a_1, a_2, …, a_k.
We can show that for given constraints the answer always exists.
Input
The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases.
The only line of each test case contains two integers n, k (3 ≤ n ≤ 10^9, 3 ≤ k ≤ n).
It is guaranteed that the sum of k over all test cases does not exceed 10^5.
Output
For each test case print k positive integers a_1, a_2, …, a_k, for which all conditions are satisfied.
Example
Input
2
6 4
9 5
Output
1 2 2 1
1 3 3 1 1
Submitted Solution:
```
import sys
import bisect
input_=lambda: sys.stdin.readline().strip("\r\n")
from math import log
sa=lambda :input_()
sb=lambda:int(input_())
sc=lambda:input_().split()
sd=lambda:list(map(int,input_().split()))
se=lambda:float(input_())
sf=lambda:list(input_())
flsh=lambda: sys.stdout.flush()
mod=10**9+7
def giver(n):
if n%2:
return [1,n//2,n//2]
else:
if int(log(n,2))==log(n,2):
return [n//2,n//4,n//4]
else:
x=list(bin(n)[2:])
t=0
s=len(x)
for i in range(len(x)-1,-1,-1):
if x[i]=='1':
break
t+=1
abe=t
while(abe>=0):
x.pop()
abe-=1
x=x+['0']*(t)
x="".join(x)
return [int(x,2),int(x,2),pow(2,t)]
def hnbhai():
n,k=sd()
ans=[1]*(k-3)+giver(n-(k-3))
print(*ans)
for _ in range(sb()):
hnbhai()
``` | instruction | 0 | 26,766 | 5 | 53,532 |
Yes | output | 1 | 26,766 | 5 | 53,533 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
It is the hard version of the problem. The only difference is that in this version 3 ≤ k ≤ n.
You are given a positive integer n. Find k positive integers a_1, a_2, …, a_k, such that:
* a_1 + a_2 + … + a_k = n
* LCM(a_1, a_2, …, a_k) ≤ n/2
Here LCM is the [least common multiple](https://en.wikipedia.org/wiki/Least_common_multiple) of numbers a_1, a_2, …, a_k.
We can show that for given constraints the answer always exists.
Input
The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases.
The only line of each test case contains two integers n, k (3 ≤ n ≤ 10^9, 3 ≤ k ≤ n).
It is guaranteed that the sum of k over all test cases does not exceed 10^5.
Output
For each test case print k positive integers a_1, a_2, …, a_k, for which all conditions are satisfied.
Example
Input
2
6 4
9 5
Output
1 2 2 1
1 3 3 1 1
Submitted Solution:
```
t = int(input())
for _ in range(t):
n, k = map(int, input().split())
n = n-(k-3)
rep = []
if n%2:
rep = [(n-1)//2, (n-1)//2, 1]
else:
if n==4:
rep = [1,1,2]
else:
v = n//2 - 1
if v%2:
rep = [n//2, n//4, n//4]
else:
rep = [v, v, 2]
rep+=[1]*(k-3)
print(*rep)
``` | instruction | 0 | 26,767 | 5 | 53,534 |
Yes | output | 1 | 26,767 | 5 | 53,535 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
It is the hard version of the problem. The only difference is that in this version 3 ≤ k ≤ n.
You are given a positive integer n. Find k positive integers a_1, a_2, …, a_k, such that:
* a_1 + a_2 + … + a_k = n
* LCM(a_1, a_2, …, a_k) ≤ n/2
Here LCM is the [least common multiple](https://en.wikipedia.org/wiki/Least_common_multiple) of numbers a_1, a_2, …, a_k.
We can show that for given constraints the answer always exists.
Input
The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases.
The only line of each test case contains two integers n, k (3 ≤ n ≤ 10^9, 3 ≤ k ≤ n).
It is guaranteed that the sum of k over all test cases does not exceed 10^5.
Output
For each test case print k positive integers a_1, a_2, …, a_k, for which all conditions are satisfied.
Example
Input
2
6 4
9 5
Output
1 2 2 1
1 3 3 1 1
Submitted Solution:
```
t = int(input())
for T in range(t):
# n = int(input())
n, k = list(map(int, input().split()))
a = []
x = k-3
for j in range(k-3):
print(1, end=" ")
n = n-k+3
if n%2==0 and n%4!=0:
print(n//2-1, n//2-1, 2)
if n%4==0 and n%2==0:
print(n//2, n//4, n//4)
if n%2!=0:
print(n//2, n//2, 1)
``` | instruction | 0 | 26,768 | 5 | 53,536 |
Yes | output | 1 | 26,768 | 5 | 53,537 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
It is the hard version of the problem. The only difference is that in this version 3 ≤ k ≤ n.
You are given a positive integer n. Find k positive integers a_1, a_2, …, a_k, such that:
* a_1 + a_2 + … + a_k = n
* LCM(a_1, a_2, …, a_k) ≤ n/2
Here LCM is the [least common multiple](https://en.wikipedia.org/wiki/Least_common_multiple) of numbers a_1, a_2, …, a_k.
We can show that for given constraints the answer always exists.
Input
The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases.
The only line of each test case contains two integers n, k (3 ≤ n ≤ 10^9, 3 ≤ k ≤ n).
It is guaranteed that the sum of k over all test cases does not exceed 10^5.
Output
For each test case print k positive integers a_1, a_2, …, a_k, for which all conditions are satisfied.
Example
Input
2
6 4
9 5
Output
1 2 2 1
1 3 3 1 1
Submitted Solution:
```
import math
for _ in range(int(input())):
n,k=map(int,input().split())
ans=[]
while n>0:
pw=int(math.log(n,2))
ans.append(2**pw)
n-=2**pw
k=k-len(ans)
for i in range(k):
ans=[ans[0]//2]+[ans[0]//2]+ans[1:]
ans.sort()
ans=ans[::-1]
print(*ans,sep=' ')
``` | instruction | 0 | 26,771 | 5 | 53,542 |
No | output | 1 | 26,771 | 5 | 53,543 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
It is the hard version of the problem. The only difference is that in this version 3 ≤ k ≤ n.
You are given a positive integer n. Find k positive integers a_1, a_2, …, a_k, such that:
* a_1 + a_2 + … + a_k = n
* LCM(a_1, a_2, …, a_k) ≤ n/2
Here LCM is the [least common multiple](https://en.wikipedia.org/wiki/Least_common_multiple) of numbers a_1, a_2, …, a_k.
We can show that for given constraints the answer always exists.
Input
The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases.
The only line of each test case contains two integers n, k (3 ≤ n ≤ 10^9, 3 ≤ k ≤ n).
It is guaranteed that the sum of k over all test cases does not exceed 10^5.
Output
For each test case print k positive integers a_1, a_2, …, a_k, for which all conditions are satisfied.
Example
Input
2
6 4
9 5
Output
1 2 2 1
1 3 3 1 1
Submitted Solution:
```
t=int(input())
for _ in range(t):
n,k=map(int,input().split())
if n%2==1:
ans=[1,(n-1)//2,(n-1)//2]
elif n%2==0 and n%4!=0:
ans=[2,(n-2)//2,(n-2)//2]
elif n%4==0:
ans=[n//2,n//4,n//4]
ins=ans
for i in range(k-3):
flag=True
for j in range(len(ins)):
if ins[j]%2==0:
ins[j]/=2
ins.append(ins[j])
flag=False
break
elif ins[j]%2==1 and ins[j]!=1:
counts=ins[j]
if flag:
ins[ins.index(counts)]-=1
ins[ins.index(counts)]-=1
ins.append(2)
ins=list(map(int,ins))
ins=list(map(str,ins))
print(' '.join(ins))
``` | instruction | 0 | 26,772 | 5 | 53,544 |
No | output | 1 | 26,772 | 5 | 53,545 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
It is the hard version of the problem. The only difference is that in this version 3 ≤ k ≤ n.
You are given a positive integer n. Find k positive integers a_1, a_2, …, a_k, such that:
* a_1 + a_2 + … + a_k = n
* LCM(a_1, a_2, …, a_k) ≤ n/2
Here LCM is the [least common multiple](https://en.wikipedia.org/wiki/Least_common_multiple) of numbers a_1, a_2, …, a_k.
We can show that for given constraints the answer always exists.
Input
The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases.
The only line of each test case contains two integers n, k (3 ≤ n ≤ 10^9, 3 ≤ k ≤ n).
It is guaranteed that the sum of k over all test cases does not exceed 10^5.
Output
For each test case print k positive integers a_1, a_2, …, a_k, for which all conditions are satisfied.
Example
Input
2
6 4
9 5
Output
1 2 2 1
1 3 3 1 1
Submitted Solution:
```
def fun(n):
if(n==3):
print(1,1,1)
elif(n>3 and n%2==1):
print(n//2,n//2,+1)
elif(n>3 and n%2==0):
if((n//2)%2==0):
print(n//2,(n//2)//2,(n//2)//2)
else:
print(n//2,(n-2)//2,(n-2)//2)
for _ in range(int(input())):
n,k=map(int,input().split())
for i in range(k-3):
print(1,end=" ")
fun(n-(k-3))
``` | instruction | 0 | 26,773 | 5 | 53,546 |
No | output | 1 | 26,773 | 5 | 53,547 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Chris is very keen on his toy blocks. His teacher, however, wants Chris to solve more problems, so he decided to play a trick on Chris.
There are exactly s blocks in Chris's set, each block has a unique number from 1 to s. Chris's teacher picks a subset of blocks X and keeps it to himself. He will give them back only if Chris can pick such a non-empty subset Y from the remaining blocks, that the equality holds:
<image> "Are you kidding me?", asks Chris.
For example, consider a case where s = 8 and Chris's teacher took the blocks with numbers 1, 4 and 5. One way for Chris to choose a set is to pick the blocks with numbers 3 and 6, see figure. Then the required sums would be equal: (1 - 1) + (4 - 1) + (5 - 1) = (8 - 3) + (8 - 6) = 7.
<image>
However, now Chris has exactly s = 106 blocks. Given the set X of blocks his teacher chooses, help Chris to find the required set Y!
Input
The first line of input contains a single integer n (1 ≤ n ≤ 5·105), the number of blocks in the set X. The next line contains n distinct space-separated integers x1, x2, ..., xn (1 ≤ xi ≤ 106), the numbers of the blocks in X.
Note: since the size of the input and output could be very large, don't use slow output techniques in your language. For example, do not use input and output streams (cin, cout) in C++.
Output
In the first line of output print a single integer m (1 ≤ m ≤ 106 - n), the number of blocks in the set Y. In the next line output m distinct space-separated integers y1, y2, ..., ym (1 ≤ yi ≤ 106), such that the required equality holds. The sets X and Y should not intersect, i.e. xi ≠ yj for all i, j (1 ≤ i ≤ n; 1 ≤ j ≤ m). It is guaranteed that at least one solution always exists. If there are multiple solutions, output any of them.
Examples
Input
3
1 4 5
Output
2
999993 1000000
Input
1
1
Output
1
1000000
Submitted Solution:
```
import sys
from math import gcd,sqrt,ceil
from collections import defaultdict,Counter,deque
import math
# input=sys.stdin.readline
# def print(x):
# sys.stdout.write(str(x)+"\n")
# sys.stdout=open("CP1/output.txt",'w')
# sys.stdin=open("CP1/input.txt",'r')
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")
# import sys
# import io, os
# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
def get_sum(bit,i):
s = 0
i+=1
while i>0:
s+=bit[i]
i-=i&(-i)
return s
def update(bit,n,i,v):
i+=1
while i<=n:
bit[i]+=v
i+=i&(-i)
def modInverse(b,m):
g = math.gcd(b, m)
if (g != 1):
return -1
else:
return pow(b, m - 2, m)
n = int(input())
l = list(map(int,input().split()))
ha = 0
for i in range(n):
ha+=l[i]-1
lo = 0
seti = set(l)
ans = []
s = 10**6
for i in range(1,10**6+1):
if i not in seti:
if s-i + lo<=ha:
lo+=s-i
ans.append(i)
if lo == ha:
break
# print(lo,ha)
print(len(ans))
print(*ans)
``` | instruction | 0 | 26,875 | 5 | 53,750 |
No | output | 1 | 26,875 | 5 | 53,751 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Chris is very keen on his toy blocks. His teacher, however, wants Chris to solve more problems, so he decided to play a trick on Chris.
There are exactly s blocks in Chris's set, each block has a unique number from 1 to s. Chris's teacher picks a subset of blocks X and keeps it to himself. He will give them back only if Chris can pick such a non-empty subset Y from the remaining blocks, that the equality holds:
<image> "Are you kidding me?", asks Chris.
For example, consider a case where s = 8 and Chris's teacher took the blocks with numbers 1, 4 and 5. One way for Chris to choose a set is to pick the blocks with numbers 3 and 6, see figure. Then the required sums would be equal: (1 - 1) + (4 - 1) + (5 - 1) = (8 - 3) + (8 - 6) = 7.
<image>
However, now Chris has exactly s = 106 blocks. Given the set X of blocks his teacher chooses, help Chris to find the required set Y!
Input
The first line of input contains a single integer n (1 ≤ n ≤ 5·105), the number of blocks in the set X. The next line contains n distinct space-separated integers x1, x2, ..., xn (1 ≤ xi ≤ 106), the numbers of the blocks in X.
Note: since the size of the input and output could be very large, don't use slow output techniques in your language. For example, do not use input and output streams (cin, cout) in C++.
Output
In the first line of output print a single integer m (1 ≤ m ≤ 106 - n), the number of blocks in the set Y. In the next line output m distinct space-separated integers y1, y2, ..., ym (1 ≤ yi ≤ 106), such that the required equality holds. The sets X and Y should not intersect, i.e. xi ≠ yj for all i, j (1 ≤ i ≤ n; 1 ≤ j ≤ m). It is guaranteed that at least one solution always exists. If there are multiple solutions, output any of them.
Examples
Input
3
1 4 5
Output
2
999993 1000000
Input
1
1
Output
1
1000000
Submitted Solution:
```
import sys
from math import gcd,sqrt,ceil
from collections import defaultdict,Counter,deque
import math
# input=sys.stdin.readline
# def print(x):
# sys.stdout.write(str(x)+"\n")
# sys.stdout=open("CP1/output.txt",'w')
# sys.stdin=open("CP1/input.txt",'r')
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")
# import sys
# import io, os
# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
def get_sum(bit,i):
s = 0
i+=1
while i>0:
s+=bit[i]
i-=i&(-i)
return s
def update(bit,n,i,v):
i+=1
while i<=n:
bit[i]+=v
i+=i&(-i)
def modInverse(b,m):
g = math.gcd(b, m)
if (g != 1):
return -1
else:
return pow(b, m - 2, m)
# print(lo,ha)
n = int(input())
l = list(map(int,input().split()))
s = 10**6
ans = set()
l = set(l)
w = 0
for i in range(1,s+1):
opp = s+1-i
if i in l and opp not in l:
ans.add(opp)
elif i in l and opp in l:
w+=1
for i in range(1,s+1):
opp = s+1-i
if w == 0:
break
if opp not in ans and i not in ans and i not in l and opp not in l:
ans.add(opp)
ans.add(i)
w-=1
print(len(ans))
print(*ans)
``` | instruction | 0 | 26,876 | 5 | 53,752 |
No | output | 1 | 26,876 | 5 | 53,753 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Chris is very keen on his toy blocks. His teacher, however, wants Chris to solve more problems, so he decided to play a trick on Chris.
There are exactly s blocks in Chris's set, each block has a unique number from 1 to s. Chris's teacher picks a subset of blocks X and keeps it to himself. He will give them back only if Chris can pick such a non-empty subset Y from the remaining blocks, that the equality holds:
<image> "Are you kidding me?", asks Chris.
For example, consider a case where s = 8 and Chris's teacher took the blocks with numbers 1, 4 and 5. One way for Chris to choose a set is to pick the blocks with numbers 3 and 6, see figure. Then the required sums would be equal: (1 - 1) + (4 - 1) + (5 - 1) = (8 - 3) + (8 - 6) = 7.
<image>
However, now Chris has exactly s = 106 blocks. Given the set X of blocks his teacher chooses, help Chris to find the required set Y!
Input
The first line of input contains a single integer n (1 ≤ n ≤ 5·105), the number of blocks in the set X. The next line contains n distinct space-separated integers x1, x2, ..., xn (1 ≤ xi ≤ 106), the numbers of the blocks in X.
Note: since the size of the input and output could be very large, don't use slow output techniques in your language. For example, do not use input and output streams (cin, cout) in C++.
Output
In the first line of output print a single integer m (1 ≤ m ≤ 106 - n), the number of blocks in the set Y. In the next line output m distinct space-separated integers y1, y2, ..., ym (1 ≤ yi ≤ 106), such that the required equality holds. The sets X and Y should not intersect, i.e. xi ≠ yj for all i, j (1 ≤ i ≤ n; 1 ≤ j ≤ m). It is guaranteed that at least one solution always exists. If there are multiple solutions, output any of them.
Examples
Input
3
1 4 5
Output
2
999993 1000000
Input
1
1
Output
1
1000000
Submitted Solution:
```
import sys
from math import gcd,sqrt,ceil
from collections import defaultdict,Counter,deque
import math
# input=sys.stdin.readline
# def print(x):
# sys.stdout.write(str(x)+"\n")
# sys.stdout=open("CP1/output.txt",'w')
# sys.stdin=open("CP1/input.txt",'r')
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")
# import sys
# import io, os
# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
def get_sum(bit,i):
s = 0
i+=1
while i>0:
s+=bit[i]
i-=i&(-i)
return s
def update(bit,n,i,v):
i+=1
while i<=n:
bit[i]+=v
i+=i&(-i)
def modInverse(b,m):
g = math.gcd(b, m)
if (g != 1):
return -1
else:
return pow(b, m - 2, m)
n = int(input())
l = list(map(int,input().split()))
ha = 0
for i in range(n):
ha+=l[i]-1
lo = 0
seti = set(l)
ans = []
s = 10**6
for i in range(1,10**6+1):
if i not in seti:
if s-i + lo<=ha:
lo+=s-i
ans.append(i)
if lo == ha:
break
# print(lo,ha)
ans.sort()
if lo!=ha:
z = ha-lo
sa = set(ans)
k = 0
cnt = 0
for i in range(len(ans)):
if 0<ans[i]-z<=s and ans[i]-z not in seti and ans[i]-z not in sa:
ans[i]-=z
break
else:
k+=ans[i]
cnt+=1
if 0<k-z<=s and k-z not in seti and k-z not in sa:
ans = ans[:cnt]
ans.append(k-z)
break
print(len(ans))
print(*ans)
``` | instruction | 0 | 26,877 | 5 | 53,754 |
No | output | 1 | 26,877 | 5 | 53,755 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Chris is very keen on his toy blocks. His teacher, however, wants Chris to solve more problems, so he decided to play a trick on Chris.
There are exactly s blocks in Chris's set, each block has a unique number from 1 to s. Chris's teacher picks a subset of blocks X and keeps it to himself. He will give them back only if Chris can pick such a non-empty subset Y from the remaining blocks, that the equality holds:
<image> "Are you kidding me?", asks Chris.
For example, consider a case where s = 8 and Chris's teacher took the blocks with numbers 1, 4 and 5. One way for Chris to choose a set is to pick the blocks with numbers 3 and 6, see figure. Then the required sums would be equal: (1 - 1) + (4 - 1) + (5 - 1) = (8 - 3) + (8 - 6) = 7.
<image>
However, now Chris has exactly s = 106 blocks. Given the set X of blocks his teacher chooses, help Chris to find the required set Y!
Input
The first line of input contains a single integer n (1 ≤ n ≤ 5·105), the number of blocks in the set X. The next line contains n distinct space-separated integers x1, x2, ..., xn (1 ≤ xi ≤ 106), the numbers of the blocks in X.
Note: since the size of the input and output could be very large, don't use slow output techniques in your language. For example, do not use input and output streams (cin, cout) in C++.
Output
In the first line of output print a single integer m (1 ≤ m ≤ 106 - n), the number of blocks in the set Y. In the next line output m distinct space-separated integers y1, y2, ..., ym (1 ≤ yi ≤ 106), such that the required equality holds. The sets X and Y should not intersect, i.e. xi ≠ yj for all i, j (1 ≤ i ≤ n; 1 ≤ j ≤ m). It is guaranteed that at least one solution always exists. If there are multiple solutions, output any of them.
Examples
Input
3
1 4 5
Output
2
999993 1000000
Input
1
1
Output
1
1000000
Submitted Solution:
```
import sys
from math import gcd,sqrt,ceil
from collections import defaultdict,Counter,deque
import math
# input=sys.stdin.readline
# def print(x):
# sys.stdout.write(str(x)+"\n")
# sys.stdout=open("CP1/output.txt",'w')
# sys.stdin=open("CP1/input.txt",'r')
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")
# import sys
# import io, os
# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
def get_sum(bit,i):
s = 0
i+=1
while i>0:
s+=bit[i]
i-=i&(-i)
return s
def update(bit,n,i,v):
i+=1
while i<=n:
bit[i]+=v
i+=i&(-i)
def modInverse(b,m):
g = math.gcd(b, m)
if (g != 1):
return -1
else:
return pow(b, m - 2, m)
n = int(input())
l = list(map(int,input().split()))
ha = 0
for i in range(n):
ha+=l[i]-1
lo = 0
seti = set(l)
ans = []
s = 10**6
for i in range(1,10**6+1):
if i not in seti:
if s-i + lo<=ha:
lo+=s-i
ans.append(i)
if lo == ha:
break
# print(lo,ha)
ans.sort()
if lo!=ha:
z = ha-lo
# ans.reverse()
if ans[-1] == s:
ans.pop()
sa = set(ans)
for i in range(len(ans)):
if z+ans[i]<=s and z+ans[i] not in seti and z+ans[i] not in sa:
ans[i]+=z
break
print(len(ans))
print(*ans)
``` | instruction | 0 | 26,878 | 5 | 53,756 |
No | output | 1 | 26,878 | 5 | 53,757 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n numbers a1, a2, ..., an. You can perform at most k operations. For each operation you can multiply one of the numbers by x. We want to make <image> as large as possible, where <image> denotes the bitwise OR.
Find the maximum possible value of <image> after performing at most k operations optimally.
Input
The first line contains three integers n, k and x (1 ≤ n ≤ 200 000, 1 ≤ k ≤ 10, 2 ≤ x ≤ 8).
The second line contains n integers a1, a2, ..., an (0 ≤ ai ≤ 109).
Output
Output the maximum value of a bitwise OR of sequence elements after performing operations.
Examples
Input
3 1 2
1 1 1
Output
3
Input
4 2 3
1 2 4 8
Output
79
Note
For the first sample, any possible choice of doing one operation will result the same three numbers 1, 1, 2 so the result is <image>.
For the second sample if we multiply 8 by 3 two times we'll get 72. In this case the numbers will become 1, 2, 4, 72 so the OR value will be 79 and is the largest possible result. | instruction | 0 | 26,937 | 5 | 53,874 |
Tags: brute force, greedy
Correct Solution:
```
n,k,x=map(int,input().split())
*a,=map(int,input().split())
l=[0]*(n+1)
r=[0]*(n+1)
for i in range(0,n):
l[i+1]=l[i]|a[i]
r[n-i-1]=r[n-i]|a[n-i-1]
num=x**k
res=-1
for i in range(0,n):
res=max(l[i]|(a[i]*num)|r[i+1],res)
print(res)
``` | output | 1 | 26,937 | 5 | 53,875 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n numbers a1, a2, ..., an. You can perform at most k operations. For each operation you can multiply one of the numbers by x. We want to make <image> as large as possible, where <image> denotes the bitwise OR.
Find the maximum possible value of <image> after performing at most k operations optimally.
Input
The first line contains three integers n, k and x (1 ≤ n ≤ 200 000, 1 ≤ k ≤ 10, 2 ≤ x ≤ 8).
The second line contains n integers a1, a2, ..., an (0 ≤ ai ≤ 109).
Output
Output the maximum value of a bitwise OR of sequence elements after performing operations.
Examples
Input
3 1 2
1 1 1
Output
3
Input
4 2 3
1 2 4 8
Output
79
Note
For the first sample, any possible choice of doing one operation will result the same three numbers 1, 1, 2 so the result is <image>.
For the second sample if we multiply 8 by 3 two times we'll get 72. In this case the numbers will become 1, 2, 4, 72 so the OR value will be 79 and is the largest possible result. | instruction | 0 | 26,938 | 5 | 53,876 |
Tags: brute force, greedy
Correct Solution:
```
n, k, x = map(int, input().split())
a = [None] + list(map(int, input().split()))
prefix = [0] * (n + 2)
suffix = [0] * (n + 2)
for i in range(1, n + 1):
prefix[i] = a[i] | prefix[i - 1]
for i in range(n, 0, -1):
suffix[i] = a[i] | suffix[i + 1]
mul = x ** k
ans = 0
for i in range(1, n + 1):
ans = max(ans, prefix[i - 1] | (a[i] * mul) | suffix[i + 1])
print(ans)
``` | output | 1 | 26,938 | 5 | 53,877 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n numbers a1, a2, ..., an. You can perform at most k operations. For each operation you can multiply one of the numbers by x. We want to make <image> as large as possible, where <image> denotes the bitwise OR.
Find the maximum possible value of <image> after performing at most k operations optimally.
Input
The first line contains three integers n, k and x (1 ≤ n ≤ 200 000, 1 ≤ k ≤ 10, 2 ≤ x ≤ 8).
The second line contains n integers a1, a2, ..., an (0 ≤ ai ≤ 109).
Output
Output the maximum value of a bitwise OR of sequence elements after performing operations.
Examples
Input
3 1 2
1 1 1
Output
3
Input
4 2 3
1 2 4 8
Output
79
Note
For the first sample, any possible choice of doing one operation will result the same three numbers 1, 1, 2 so the result is <image>.
For the second sample if we multiply 8 by 3 two times we'll get 72. In this case the numbers will become 1, 2, 4, 72 so the OR value will be 79 and is the largest possible result. | instruction | 0 | 26,939 | 5 | 53,878 |
Tags: brute force, greedy
Correct Solution:
```
#!/usr/bin/env python
# 579D_or.py - Codeforces.com/problemset/problem/579/D by Sergey 2015
import unittest
import sys
###############################################################################
# Or Class (Main Program)
###############################################################################
class Or:
""" Or representation """
def __init__(self, test_inputs=None):
""" Default constructor """
it = iter(test_inputs.split("\n")) if test_inputs else None
def uinput():
return next(it) if it else sys.stdin.readline().rstrip()
# Reading single elements
[self.n, self.k, self.x] = map(int, uinput().split())
# Reading a single line of multiple elements
self.nums = list(map(int, uinput().split()))
self.cnt = [0] * 100
for n in self.nums:
i = 0
while n != 0:
if n % 2:
self.cnt[i] += 1
n >>= 1
i += 1
self.nmax = 0
for n in self.nums:
cur_cnt = list(self.cnt)
i = 0
nn = n
while n != 0:
if n % 2:
cur_cnt[i] -= 1
n >>= 1
i += 1
n = nn * self.x ** self.k
i = 0
while n != 0:
if n % 2:
cur_cnt[i] += 1
n >>= 1
i += 1
k = 0
for i in range(len(cur_cnt)):
if cur_cnt[i] > 0:
k += 1 << i
if k > self.nmax:
self.nmax = k
def calculate(self):
""" Main calcualtion function of the class """
result = self.nmax
return str(result)
###############################################################################
# Unit Tests
###############################################################################
class unitTests(unittest.TestCase):
def test_single_test(self):
""" Or class testing """
# Constructor test
test = "3 1 2\n1 1 1"
d = Or(test)
self.assertEqual(d.n, 3)
self.assertEqual(d.k, 1)
self.assertEqual(d.x, 2)
self.assertEqual(d.nums, [1, 1, 1])
# Sample test
self.assertEqual(Or(test).calculate(), "3")
# Sample test
test = "4 2 3\n1 2 4 8"
self.assertEqual(Or(test).calculate(), "79")
# Sample test
test = ""
# self.assertEqual(Or(test).calculate(), "0")
# My tests
test = ""
# self.assertEqual(Or(test).calculate(), "0")
# Time limit test
# self.time_limit_test(5000)
def time_limit_test(self, nmax):
""" Timelimit testing """
import random
import timeit
# Random inputs
test = str(nmax) + " " + str(nmax) + "\n"
numnums = [str(i) + " " + str(i+1) for i in range(nmax)]
test += "\n".join(numnums) + "\n"
nums = [random.randint(1, 10000) for i in range(nmax)]
test += " ".join(map(str, nums)) + "\n"
# Run the test
start = timeit.default_timer()
d = Or(test)
calc = timeit.default_timer()
d.calculate()
stop = timeit.default_timer()
print("\nTimelimit Test: " +
"{0:.3f}s (init {1:.3f}s calc {2:.3f}s)".
format(stop-start, calc-start, stop-calc))
if __name__ == "__main__":
# Avoiding recursion limitaions
sys.setrecursionlimit(100000)
if sys.argv[-1] == "-ut":
unittest.main(argv=[" "])
# Print the result string
sys.stdout.write(Or().calculate())
``` | output | 1 | 26,939 | 5 | 53,879 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n numbers a1, a2, ..., an. You can perform at most k operations. For each operation you can multiply one of the numbers by x. We want to make <image> as large as possible, where <image> denotes the bitwise OR.
Find the maximum possible value of <image> after performing at most k operations optimally.
Input
The first line contains three integers n, k and x (1 ≤ n ≤ 200 000, 1 ≤ k ≤ 10, 2 ≤ x ≤ 8).
The second line contains n integers a1, a2, ..., an (0 ≤ ai ≤ 109).
Output
Output the maximum value of a bitwise OR of sequence elements after performing operations.
Examples
Input
3 1 2
1 1 1
Output
3
Input
4 2 3
1 2 4 8
Output
79
Note
For the first sample, any possible choice of doing one operation will result the same three numbers 1, 1, 2 so the result is <image>.
For the second sample if we multiply 8 by 3 two times we'll get 72. In this case the numbers will become 1, 2, 4, 72 so the OR value will be 79 and is the largest possible result. | instruction | 0 | 26,940 | 5 | 53,880 |
Tags: brute force, greedy
Correct Solution:
```
n,k,x = map( int,input().split() )
*Arr, = map( int,input().split() )
Prfx = [0]*(n+2)
Sffx = [0]*(n+2)
for i in range(0,n):
Prfx[i+1] = Prfx[i]|Arr[i]
Sffx[n-i-1] = Sffx[n-i]|Arr[n-i-1]
now = x**k
Res = 0
for i in range(0,n):
Res = max( Prfx[i]|(Arr[i]*now)|Sffx[i+1],Res );
print(Res)
``` | output | 1 | 26,940 | 5 | 53,881 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n numbers a1, a2, ..., an. You can perform at most k operations. For each operation you can multiply one of the numbers by x. We want to make <image> as large as possible, where <image> denotes the bitwise OR.
Find the maximum possible value of <image> after performing at most k operations optimally.
Input
The first line contains three integers n, k and x (1 ≤ n ≤ 200 000, 1 ≤ k ≤ 10, 2 ≤ x ≤ 8).
The second line contains n integers a1, a2, ..., an (0 ≤ ai ≤ 109).
Output
Output the maximum value of a bitwise OR of sequence elements after performing operations.
Examples
Input
3 1 2
1 1 1
Output
3
Input
4 2 3
1 2 4 8
Output
79
Note
For the first sample, any possible choice of doing one operation will result the same three numbers 1, 1, 2 so the result is <image>.
For the second sample if we multiply 8 by 3 two times we'll get 72. In this case the numbers will become 1, 2, 4, 72 so the OR value will be 79 and is the largest possible result. | instruction | 0 | 26,941 | 5 | 53,882 |
Tags: brute force, greedy
Correct Solution:
```
import sys
class IoTool: # a tool for input redirection
DEBUG = 0
def _reader_dbg():
with open('./input.txt', 'r') as f:
lines = f.readlines()
for l in lines: yield l.strip()
def _reader_oj():
return iter(sys.stdin.read().split('\n'))
reader = _reader_dbg() if DEBUG else _reader_oj()
def read(): return next(IoTool.reader)
input = IoTool.read
def main():
n, k, x = map(int, input().split())
a = list(map(int, input().split()))
mul = 1
for i in range(k): mul *= x
if n == 1:
print(a[0] * mul)
return
pre, tail = [0] * n, [0] * n
pre[0] = a[0]
tail[n-1] = a[n-1]
for i in range(1, n): pre[i] = pre[i-1] | a[i]
for i in range(n-2, -1, -1): tail[i] = tail[i+1] | a[i]
answer = max((pre[0]*mul) | tail[1], pre[n-2]|(tail[n-1]*mul))
for i in range(1, n-1):
answer = max(answer, (a[i] * mul) | pre[i-1] | tail[i+1])
print(answer)
if __name__ == "__main__":
main()
``` | output | 1 | 26,941 | 5 | 53,883 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n numbers a1, a2, ..., an. You can perform at most k operations. For each operation you can multiply one of the numbers by x. We want to make <image> as large as possible, where <image> denotes the bitwise OR.
Find the maximum possible value of <image> after performing at most k operations optimally.
Input
The first line contains three integers n, k and x (1 ≤ n ≤ 200 000, 1 ≤ k ≤ 10, 2 ≤ x ≤ 8).
The second line contains n integers a1, a2, ..., an (0 ≤ ai ≤ 109).
Output
Output the maximum value of a bitwise OR of sequence elements after performing operations.
Examples
Input
3 1 2
1 1 1
Output
3
Input
4 2 3
1 2 4 8
Output
79
Note
For the first sample, any possible choice of doing one operation will result the same three numbers 1, 1, 2 so the result is <image>.
For the second sample if we multiply 8 by 3 two times we'll get 72. In this case the numbers will become 1, 2, 4, 72 so the OR value will be 79 and is the largest possible result. | instruction | 0 | 26,942 | 5 | 53,884 |
Tags: brute force, greedy
Correct Solution:
```
#!/usr/bin/env python
# 579D_or.py - Codeforces.com/problemset/problem/579/D by Sergey 2015
import unittest
import sys
###############################################################################
# Or Class (Main Program)
###############################################################################
class Or:
""" Or representation """
def __init__(self, test_inputs=None):
""" Default constructor """
it = iter(test_inputs.split("\n")) if test_inputs else None
def uinput():
return next(it) if it else input().rstrip()
# Reading single elements
[self.n, self.k, self.x] = map(int, uinput().split())
# Reading a single line of multiple elements
self.nums = list(map(int, uinput().split()))
self.cnt = [0] * 100
for n in self.nums:
i = 0
while n != 0:
if n % 2:
self.cnt[i] += 1
n >>= 1
i += 1
self.nmax = 0
for n in self.nums:
cur_cnt = list(self.cnt)
i = 0
nn = n
while n != 0:
if n % 2:
cur_cnt[i] -= 1
n >>= 1
i += 1
n = nn * self.x ** self.k
i = 0
while n != 0:
if n % 2:
cur_cnt[i] += 1
n >>= 1
i += 1
k = 0
for i in range(len(cur_cnt)):
if cur_cnt[i] > 0:
k += 1 << i
if k > self.nmax:
self.nmax = k
def calculate(self):
""" Main calcualtion function of the class """
result = self.nmax
return str(result)
###############################################################################
# Unit Tests
###############################################################################
class unitTests(unittest.TestCase):
def test_single_test(self):
""" Or class testing """
# Constructor test
test = "3 1 2\n1 1 1"
d = Or(test)
self.assertEqual(d.n, 3)
self.assertEqual(d.k, 1)
self.assertEqual(d.x, 2)
self.assertEqual(d.nums, [1, 1, 1])
# Sample test
self.assertEqual(Or(test).calculate(), "3")
# Sample test
test = "4 2 3\n1 2 4 8"
self.assertEqual(Or(test).calculate(), "79")
# Sample test
test = ""
# self.assertEqual(Or(test).calculate(), "0")
# My tests
test = ""
# self.assertEqual(Or(test).calculate(), "0")
# Time limit test
# self.time_limit_test(5000)
def time_limit_test(self, nmax):
""" Timelimit testing """
import random
import timeit
# Random inputs
test = str(nmax) + " " + str(nmax) + "\n"
numnums = [str(i) + " " + str(i+1) for i in range(nmax)]
test += "\n".join(numnums) + "\n"
nums = [random.randint(1, 10000) for i in range(nmax)]
test += " ".join(map(str, nums)) + "\n"
# Run the test
start = timeit.default_timer()
d = Or(test)
calc = timeit.default_timer()
d.calculate()
stop = timeit.default_timer()
print("\nTimelimit Test: " +
"{0:.3f}s (init {1:.3f}s calc {2:.3f}s)".
format(stop-start, calc-start, stop-calc))
if __name__ == "__main__":
# Avoiding recursion limitaions
sys.setrecursionlimit(100000)
if sys.argv[-1] == "-ut":
unittest.main(argv=[" "])
# Print the result string
sys.stdout.write(Or().calculate())
``` | output | 1 | 26,942 | 5 | 53,885 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n numbers a1, a2, ..., an. You can perform at most k operations. For each operation you can multiply one of the numbers by x. We want to make <image> as large as possible, where <image> denotes the bitwise OR.
Find the maximum possible value of <image> after performing at most k operations optimally.
Input
The first line contains three integers n, k and x (1 ≤ n ≤ 200 000, 1 ≤ k ≤ 10, 2 ≤ x ≤ 8).
The second line contains n integers a1, a2, ..., an (0 ≤ ai ≤ 109).
Output
Output the maximum value of a bitwise OR of sequence elements after performing operations.
Examples
Input
3 1 2
1 1 1
Output
3
Input
4 2 3
1 2 4 8
Output
79
Note
For the first sample, any possible choice of doing one operation will result the same three numbers 1, 1, 2 so the result is <image>.
For the second sample if we multiply 8 by 3 two times we'll get 72. In this case the numbers will become 1, 2, 4, 72 so the OR value will be 79 and is the largest possible result. | instruction | 0 | 26,943 | 5 | 53,886 |
Tags: brute force, greedy
Correct Solution:
```
# -*- coding:utf-8 -*-
"""
created by shuangquan.huang at 1/10/20
a simple conclusion is that we should multiple only one v with x K times
"""
import collections
import time
import os
import sys
import bisect
import heapq
from typing import List
def solve(N, K, X, A):
prefix = [0 for _ in range(N)]
suffix = [0 for _ in range(N)]
for i, v in enumerate(A):
prefix[i] = (prefix[i-1] if i-1 >= 0 else 0) | v
for i in range(N-1, -1, -1):
suffix[i] = (suffix[i+1] if i+1 < N else 0) | A[i]
ans = 0
for i, v in enumerate(A):
a = prefix[i-1] if i-1 >= 0 else 0
b = suffix[i+1] if i+1 < N else 0
ans = max(ans, a | b | (v * X**K))
return ans
N, K, X = map(int, input().split())
A = [int(x) for x in input().split()]
print(solve(N, K, X, A))
``` | output | 1 | 26,943 | 5 | 53,887 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n numbers a1, a2, ..., an. You can perform at most k operations. For each operation you can multiply one of the numbers by x. We want to make <image> as large as possible, where <image> denotes the bitwise OR.
Find the maximum possible value of <image> after performing at most k operations optimally.
Input
The first line contains three integers n, k and x (1 ≤ n ≤ 200 000, 1 ≤ k ≤ 10, 2 ≤ x ≤ 8).
The second line contains n integers a1, a2, ..., an (0 ≤ ai ≤ 109).
Output
Output the maximum value of a bitwise OR of sequence elements after performing operations.
Examples
Input
3 1 2
1 1 1
Output
3
Input
4 2 3
1 2 4 8
Output
79
Note
For the first sample, any possible choice of doing one operation will result the same three numbers 1, 1, 2 so the result is <image>.
For the second sample if we multiply 8 by 3 two times we'll get 72. In this case the numbers will become 1, 2, 4, 72 so the OR value will be 79 and is the largest possible result. | instruction | 0 | 26,944 | 5 | 53,888 |
Tags: brute force, greedy
Correct Solution:
```
n, k, x = map(int, input().split())
a = list(map(int, input().split()))
x = x ** k
pref, suff = [0]*n, [0]*n
for i in range(n - 1):
pref[i + 1] = a[i] | pref[i]
for i in range(n - 1, 0, -1):
suff[i - 1] = a[i] | suff[i]
res = 0
for i in range(n):
res = max(res, (a[i] * x) | pref[i] | suff[i])
print(res)
``` | output | 1 | 26,944 | 5 | 53,889 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given n numbers a1, a2, ..., an. You can perform at most k operations. For each operation you can multiply one of the numbers by x. We want to make <image> as large as possible, where <image> denotes the bitwise OR.
Find the maximum possible value of <image> after performing at most k operations optimally.
Input
The first line contains three integers n, k and x (1 ≤ n ≤ 200 000, 1 ≤ k ≤ 10, 2 ≤ x ≤ 8).
The second line contains n integers a1, a2, ..., an (0 ≤ ai ≤ 109).
Output
Output the maximum value of a bitwise OR of sequence elements after performing operations.
Examples
Input
3 1 2
1 1 1
Output
3
Input
4 2 3
1 2 4 8
Output
79
Note
For the first sample, any possible choice of doing one operation will result the same three numbers 1, 1, 2 so the result is <image>.
For the second sample if we multiply 8 by 3 two times we'll get 72. In this case the numbers will become 1, 2, 4, 72 so the OR value will be 79 and is the largest possible result.
Submitted Solution:
```
import sys
def get_ints(): return list(map(int, sys.stdin.readline().strip().split()))
def solve(N, K, X, A):
prefix, suffix = [0] * (N + 2), [0] * (N + 2)
for i in range(N):
prefix[i + 1] = prefix[i] | A[i]
for i in range(N - 1, -1, -1):
suffix[i] = suffix[i + 1] | A[i]
ans = 0
val = X ** K
for i in range(N):
ans = max(
ans,
prefix[i] | A[i] * val | suffix[i + 1]
)
return ans
N, K, X = map(int, input().split())
A = get_ints()
print(solve(N, K, X, A))
``` | instruction | 0 | 26,945 | 5 | 53,890 |
Yes | output | 1 | 26,945 | 5 | 53,891 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given n numbers a1, a2, ..., an. You can perform at most k operations. For each operation you can multiply one of the numbers by x. We want to make <image> as large as possible, where <image> denotes the bitwise OR.
Find the maximum possible value of <image> after performing at most k operations optimally.
Input
The first line contains three integers n, k and x (1 ≤ n ≤ 200 000, 1 ≤ k ≤ 10, 2 ≤ x ≤ 8).
The second line contains n integers a1, a2, ..., an (0 ≤ ai ≤ 109).
Output
Output the maximum value of a bitwise OR of sequence elements after performing operations.
Examples
Input
3 1 2
1 1 1
Output
3
Input
4 2 3
1 2 4 8
Output
79
Note
For the first sample, any possible choice of doing one operation will result the same three numbers 1, 1, 2 so the result is <image>.
For the second sample if we multiply 8 by 3 two times we'll get 72. In this case the numbers will become 1, 2, 4, 72 so the OR value will be 79 and is the largest possible result.
Submitted Solution:
```
__author__ = 'kitkat'
import sys
#sys.stdin = open("in.txt")
try:
while True:
n, k, x = map(int, input().split(" "))
val = [0] + list(map(int, input().split(" ")))
res = 0
L = [0 for i in range(200003)]
R = [0 for i in range(200003)]
for i in range(1, n+1, 1):
L[i] = L[i-1] | val[i]
R[n-i+1] = R[n-i+2] | val[n-i+1]
for i in range(1, n+1, 1):
for j in range(k):
val[i] *= x
for i in range(1, n+1, 1):
res = max(res, L[i-1] | R[i+1] | val[i])
print(res)
except EOFError:
pass
``` | instruction | 0 | 26,946 | 5 | 53,892 |
Yes | output | 1 | 26,946 | 5 | 53,893 |
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