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.
You are given an integer n (n β₯ 0) represented with k digits in base (radix) b. So,
$$$n = a_1 β
b^{k-1} + a_2 β
b^{k-2} + β¦ a_{k-1} β
b + a_k.$$$
For example, if b=17, k=3 and a=[11, 15, 7] then n=11β
17^2+15β
17+7=3179+255+7=3441.
Determine whether n is even or odd.
Input
The first line contains two integers b and k (2β€ bβ€ 100, 1β€ kβ€ 10^5) β the base of the number and the number of digits.
The second line contains k integers a_1, a_2, β¦, a_k (0β€ a_i < b) β the digits of n.
The representation of n contains no unnecessary leading zero. That is, a_1 can be equal to 0 only if k = 1.
Output
Print "even" if n is even, otherwise print "odd".
You can print each letter in any case (upper or lower).
Examples
Input
13 3
3 2 7
Output
even
Input
10 9
1 2 3 4 5 6 7 8 9
Output
odd
Input
99 5
32 92 85 74 4
Output
odd
Input
2 2
1 0
Output
even
Note
In the first example, n = 3 β
13^2 + 2 β
13 + 7 = 540, which is even.
In the second example, n = 123456789 is odd.
In the third example, n = 32 β
99^4 + 92 β
99^3 + 85 β
99^2 + 74 β
99 + 4 = 3164015155 is odd.
In the fourth example n = 2.
Submitted Solution:
```
b, k = [int(i) for i in input().split()]
arr = [int(i) for i in input().split()]
odd = 0
for i in arr:
if b & 1 or i & 1: odd += 1
if odd & 1: print('odd')
else: print('even')
``` | instruction | 0 | 98,655 | 5 | 197,310 |
No | output | 1 | 98,655 | 5 | 197,311 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an integer n (n β₯ 0) represented with k digits in base (radix) b. So,
$$$n = a_1 β
b^{k-1} + a_2 β
b^{k-2} + β¦ a_{k-1} β
b + a_k.$$$
For example, if b=17, k=3 and a=[11, 15, 7] then n=11β
17^2+15β
17+7=3179+255+7=3441.
Determine whether n is even or odd.
Input
The first line contains two integers b and k (2β€ bβ€ 100, 1β€ kβ€ 10^5) β the base of the number and the number of digits.
The second line contains k integers a_1, a_2, β¦, a_k (0β€ a_i < b) β the digits of n.
The representation of n contains no unnecessary leading zero. That is, a_1 can be equal to 0 only if k = 1.
Output
Print "even" if n is even, otherwise print "odd".
You can print each letter in any case (upper or lower).
Examples
Input
13 3
3 2 7
Output
even
Input
10 9
1 2 3 4 5 6 7 8 9
Output
odd
Input
99 5
32 92 85 74 4
Output
odd
Input
2 2
1 0
Output
even
Note
In the first example, n = 3 β
13^2 + 2 β
13 + 7 = 540, which is even.
In the second example, n = 123456789 is odd.
In the third example, n = 32 β
99^4 + 92 β
99^3 + 85 β
99^2 + 74 β
99 + 4 = 3164015155 is odd.
In the fourth example n = 2.
Submitted Solution:
```
k, n = [int(i) for i in input().split()]
a = [int(i) for i in input().split()]
if len(a) != 1:
if a[len(a) - 1] % 2 == 1:
if k % 2 == 1:
print('even')
else:
print('odd')
else:
if k % 2 == 1:
print('odd')
else:
print('even')
else:
if a[len(a) - 1] % 2 == 0:
print('even')
else:
print('odd')
``` | instruction | 0 | 98,656 | 5 | 197,312 |
No | output | 1 | 98,656 | 5 | 197,313 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Greatest Secret Ever consists of n words, indexed by positive integers from 1 to n. The secret needs dividing between k Keepers (let's index them by positive integers from 1 to k), the i-th Keeper gets a non-empty set of words with numbers from the set Ui = (ui, 1, ui, 2, ..., ui, |Ui|). Here and below we'll presuppose that the set elements are written in the increasing order.
We'll say that the secret is safe if the following conditions are hold:
* for any two indexes i, j (1 β€ i < j β€ k) the intersection of sets Ui and Uj is an empty set;
* the union of sets U1, U2, ..., Uk is set (1, 2, ..., n);
* in each set Ui, its elements ui, 1, ui, 2, ..., ui, |Ui| do not form an arithmetic progression (in particular, |Ui| β₯ 3 should hold).
Let us remind you that the elements of set (u1, u2, ..., us) form an arithmetic progression if there is such number d, that for all i (1 β€ i < s) fulfills ui + d = ui + 1. For example, the elements of sets (5), (1, 10) and (1, 5, 9) form arithmetic progressions and the elements of sets (1, 2, 4) and (3, 6, 8) don't.
Your task is to find any partition of the set of words into subsets U1, U2, ..., Uk so that the secret is safe. Otherwise indicate that there's no such partition.
Input
The input consists of a single line which contains two integers n and k (2 β€ k β€ n β€ 106) β the number of words in the secret and the number of the Keepers. The numbers are separated by a single space.
Output
If there is no way to keep the secret safe, print a single integer "-1" (without the quotes). Otherwise, print n integers, the i-th of them representing the number of the Keeper who's got the i-th word of the secret.
If there are multiple solutions, print any of them.
Examples
Input
11 3
Output
3 1 2 1 1 2 3 2 2 3 1
Input
5 2
Output
-1
Submitted Solution:
```
n, k = map(int, input().split())
div_size = n // k
if div_size < 3:
print(-1)
else:
keepers = []
for i in range(k):
keepers.append(i + 1)
for i in range(k):
for _ in range(div_size - 1):
keepers.append(i + 1)
shortage = n - len(keepers)
for _ in range(shortage):
keepers.append(k)
print(*keepers)
``` | instruction | 0 | 98,936 | 5 | 197,872 |
Yes | output | 1 | 98,936 | 5 | 197,873 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Greatest Secret Ever consists of n words, indexed by positive integers from 1 to n. The secret needs dividing between k Keepers (let's index them by positive integers from 1 to k), the i-th Keeper gets a non-empty set of words with numbers from the set Ui = (ui, 1, ui, 2, ..., ui, |Ui|). Here and below we'll presuppose that the set elements are written in the increasing order.
We'll say that the secret is safe if the following conditions are hold:
* for any two indexes i, j (1 β€ i < j β€ k) the intersection of sets Ui and Uj is an empty set;
* the union of sets U1, U2, ..., Uk is set (1, 2, ..., n);
* in each set Ui, its elements ui, 1, ui, 2, ..., ui, |Ui| do not form an arithmetic progression (in particular, |Ui| β₯ 3 should hold).
Let us remind you that the elements of set (u1, u2, ..., us) form an arithmetic progression if there is such number d, that for all i (1 β€ i < s) fulfills ui + d = ui + 1. For example, the elements of sets (5), (1, 10) and (1, 5, 9) form arithmetic progressions and the elements of sets (1, 2, 4) and (3, 6, 8) don't.
Your task is to find any partition of the set of words into subsets U1, U2, ..., Uk so that the secret is safe. Otherwise indicate that there's no such partition.
Input
The input consists of a single line which contains two integers n and k (2 β€ k β€ n β€ 106) β the number of words in the secret and the number of the Keepers. The numbers are separated by a single space.
Output
If there is no way to keep the secret safe, print a single integer "-1" (without the quotes). Otherwise, print n integers, the i-th of them representing the number of the Keeper who's got the i-th word of the secret.
If there are multiple solutions, print any of them.
Examples
Input
11 3
Output
3 1 2 1 1 2 3 2 2 3 1
Input
5 2
Output
-1
Submitted Solution:
```
import sys
def solve():
n, k = map(int, input().split())
if n // k < 3 or n < 6:
print(-1)
return
res = list()
for i in range(1, k + 1):
res.append(i)
res.append(i)
for i in range(1, k + 1):
res.append(i)
while len(res) < n: res.append(1);
print(" ".join(map(str, res)))
solve()
``` | instruction | 0 | 98,937 | 5 | 197,874 |
Yes | output | 1 | 98,937 | 5 | 197,875 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Greatest Secret Ever consists of n words, indexed by positive integers from 1 to n. The secret needs dividing between k Keepers (let's index them by positive integers from 1 to k), the i-th Keeper gets a non-empty set of words with numbers from the set Ui = (ui, 1, ui, 2, ..., ui, |Ui|). Here and below we'll presuppose that the set elements are written in the increasing order.
We'll say that the secret is safe if the following conditions are hold:
* for any two indexes i, j (1 β€ i < j β€ k) the intersection of sets Ui and Uj is an empty set;
* the union of sets U1, U2, ..., Uk is set (1, 2, ..., n);
* in each set Ui, its elements ui, 1, ui, 2, ..., ui, |Ui| do not form an arithmetic progression (in particular, |Ui| β₯ 3 should hold).
Let us remind you that the elements of set (u1, u2, ..., us) form an arithmetic progression if there is such number d, that for all i (1 β€ i < s) fulfills ui + d = ui + 1. For example, the elements of sets (5), (1, 10) and (1, 5, 9) form arithmetic progressions and the elements of sets (1, 2, 4) and (3, 6, 8) don't.
Your task is to find any partition of the set of words into subsets U1, U2, ..., Uk so that the secret is safe. Otherwise indicate that there's no such partition.
Input
The input consists of a single line which contains two integers n and k (2 β€ k β€ n β€ 106) β the number of words in the secret and the number of the Keepers. The numbers are separated by a single space.
Output
If there is no way to keep the secret safe, print a single integer "-1" (without the quotes). Otherwise, print n integers, the i-th of them representing the number of the Keeper who's got the i-th word of the secret.
If there are multiple solutions, print any of them.
Examples
Input
11 3
Output
3 1 2 1 1 2 3 2 2 3 1
Input
5 2
Output
-1
Submitted Solution:
```
n, k = map(int, input().split())
if n < 3 * k: print(-1)
else:
d = n // k
p = [min(1 + i // d, k) for i in range(n)]
for i in range(d, n, 2 * d):
p[i], p[i - 1] = p[i - 1], p[i]
if k > 2: p[0], p[-1] = p[-1], p[0]
print(' '.join(str(i) for i in p))
``` | instruction | 0 | 98,938 | 5 | 197,876 |
Yes | output | 1 | 98,938 | 5 | 197,877 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Greatest Secret Ever consists of n words, indexed by positive integers from 1 to n. The secret needs dividing between k Keepers (let's index them by positive integers from 1 to k), the i-th Keeper gets a non-empty set of words with numbers from the set Ui = (ui, 1, ui, 2, ..., ui, |Ui|). Here and below we'll presuppose that the set elements are written in the increasing order.
We'll say that the secret is safe if the following conditions are hold:
* for any two indexes i, j (1 β€ i < j β€ k) the intersection of sets Ui and Uj is an empty set;
* the union of sets U1, U2, ..., Uk is set (1, 2, ..., n);
* in each set Ui, its elements ui, 1, ui, 2, ..., ui, |Ui| do not form an arithmetic progression (in particular, |Ui| β₯ 3 should hold).
Let us remind you that the elements of set (u1, u2, ..., us) form an arithmetic progression if there is such number d, that for all i (1 β€ i < s) fulfills ui + d = ui + 1. For example, the elements of sets (5), (1, 10) and (1, 5, 9) form arithmetic progressions and the elements of sets (1, 2, 4) and (3, 6, 8) don't.
Your task is to find any partition of the set of words into subsets U1, U2, ..., Uk so that the secret is safe. Otherwise indicate that there's no such partition.
Input
The input consists of a single line which contains two integers n and k (2 β€ k β€ n β€ 106) β the number of words in the secret and the number of the Keepers. The numbers are separated by a single space.
Output
If there is no way to keep the secret safe, print a single integer "-1" (without the quotes). Otherwise, print n integers, the i-th of them representing the number of the Keeper who's got the i-th word of the secret.
If there are multiple solutions, print any of them.
Examples
Input
11 3
Output
3 1 2 1 1 2 3 2 2 3 1
Input
5 2
Output
-1
Submitted Solution:
```
n, k = map(int, input().split())
if k * 3 > n:
print(-1)
else:
ans = []
for i in range(1, k * 2 + 1):
ans.append(k if i % k == 0 else i % k)
if k % 2:
ans.append(k)
for i in range(k - 1, 0, -1):
if i % 2:
ans.append(ans[-1] + i)
else:
ans.append(ans[-1] - i)
else:
ans.extend([i for i in range(k, 0, -1)])
ans.extend([(k - (i % k)) for i in range(k * 3 + 1, n + 1)])
print(*ans)
``` | instruction | 0 | 98,939 | 5 | 197,878 |
Yes | output | 1 | 98,939 | 5 | 197,879 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Greatest Secret Ever consists of n words, indexed by positive integers from 1 to n. The secret needs dividing between k Keepers (let's index them by positive integers from 1 to k), the i-th Keeper gets a non-empty set of words with numbers from the set Ui = (ui, 1, ui, 2, ..., ui, |Ui|). Here and below we'll presuppose that the set elements are written in the increasing order.
We'll say that the secret is safe if the following conditions are hold:
* for any two indexes i, j (1 β€ i < j β€ k) the intersection of sets Ui and Uj is an empty set;
* the union of sets U1, U2, ..., Uk is set (1, 2, ..., n);
* in each set Ui, its elements ui, 1, ui, 2, ..., ui, |Ui| do not form an arithmetic progression (in particular, |Ui| β₯ 3 should hold).
Let us remind you that the elements of set (u1, u2, ..., us) form an arithmetic progression if there is such number d, that for all i (1 β€ i < s) fulfills ui + d = ui + 1. For example, the elements of sets (5), (1, 10) and (1, 5, 9) form arithmetic progressions and the elements of sets (1, 2, 4) and (3, 6, 8) don't.
Your task is to find any partition of the set of words into subsets U1, U2, ..., Uk so that the secret is safe. Otherwise indicate that there's no such partition.
Input
The input consists of a single line which contains two integers n and k (2 β€ k β€ n β€ 106) β the number of words in the secret and the number of the Keepers. The numbers are separated by a single space.
Output
If there is no way to keep the secret safe, print a single integer "-1" (without the quotes). Otherwise, print n integers, the i-th of them representing the number of the Keeper who's got the i-th word of the secret.
If there are multiple solutions, print any of them.
Examples
Input
11 3
Output
3 1 2 1 1 2 3 2 2 3 1
Input
5 2
Output
-1
Submitted Solution:
```
n, k = map(int, input().split())
if k * 3 < k:
print(-1)
else:
ans = []
for i in range(1, k * 2 + 1):
ans.append(k if i % k == 0 else i % k)
if k % 2:
ans.append(k)
for i in range(k - 1, 0, -1):
if i % 2:
ans.append(ans[-1] + i)
else:
ans.append(ans[-1] - i)
else:
ans.extend([i for i in range(k, 0, -1)])
ans.extend([(k - (i % k)) for i in range(k * 3 + 1, n + 1)])
print(*ans)
``` | instruction | 0 | 98,940 | 5 | 197,880 |
No | output | 1 | 98,940 | 5 | 197,881 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Greatest Secret Ever consists of n words, indexed by positive integers from 1 to n. The secret needs dividing between k Keepers (let's index them by positive integers from 1 to k), the i-th Keeper gets a non-empty set of words with numbers from the set Ui = (ui, 1, ui, 2, ..., ui, |Ui|). Here and below we'll presuppose that the set elements are written in the increasing order.
We'll say that the secret is safe if the following conditions are hold:
* for any two indexes i, j (1 β€ i < j β€ k) the intersection of sets Ui and Uj is an empty set;
* the union of sets U1, U2, ..., Uk is set (1, 2, ..., n);
* in each set Ui, its elements ui, 1, ui, 2, ..., ui, |Ui| do not form an arithmetic progression (in particular, |Ui| β₯ 3 should hold).
Let us remind you that the elements of set (u1, u2, ..., us) form an arithmetic progression if there is such number d, that for all i (1 β€ i < s) fulfills ui + d = ui + 1. For example, the elements of sets (5), (1, 10) and (1, 5, 9) form arithmetic progressions and the elements of sets (1, 2, 4) and (3, 6, 8) don't.
Your task is to find any partition of the set of words into subsets U1, U2, ..., Uk so that the secret is safe. Otherwise indicate that there's no such partition.
Input
The input consists of a single line which contains two integers n and k (2 β€ k β€ n β€ 106) β the number of words in the secret and the number of the Keepers. The numbers are separated by a single space.
Output
If there is no way to keep the secret safe, print a single integer "-1" (without the quotes). Otherwise, print n integers, the i-th of them representing the number of the Keeper who's got the i-th word of the secret.
If there are multiple solutions, print any of them.
Examples
Input
11 3
Output
3 1 2 1 1 2 3 2 2 3 1
Input
5 2
Output
-1
Submitted Solution:
```
n, k = map(int, input().split())
if k * 3 < n:
print(-1)
exit(0)
ans = [0] * n
if n % k == 0 and (n // k) % 2 == 1:
if n == 3:
print(-1)
exit(0)
l = n - (n % 6) - 6
l = max(0, l)
filled = 0
f, s = 1, 2
for i in range(l):
if f > k:
f = 1
if s > k:
s = 1
if filled == k:
break
j = i % 6
r = [f, f, s, f, s, s][j]
ans[i] = j
if j == 5:
f, s = f + 2, s + 2
filled += 1
if j == 3:
filled += 1
tail = [k - 2, k - 2, k, k - 2, k - 1, k - 1, k, k, k - 1]
for i in range(9):
ans[l + i] = tail[i]
else:
filled = 0
f, s = 1, 2
for i in range(n):
if f > k:
f = 1
if s > k:
s = 1
if filled == k:
break
j = i % 6
r = [f, f, s, f, s, s][j]
ans[i] = j
if j == 5:
f, s = f + 2, s + 2
filled += 1
if j == 3:
filled += 1
for z in range(i, n):
ans[z] = 1
print(*ans)
``` | instruction | 0 | 98,941 | 5 | 197,882 |
No | output | 1 | 98,941 | 5 | 197,883 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Greatest Secret Ever consists of n words, indexed by positive integers from 1 to n. The secret needs dividing between k Keepers (let's index them by positive integers from 1 to k), the i-th Keeper gets a non-empty set of words with numbers from the set Ui = (ui, 1, ui, 2, ..., ui, |Ui|). Here and below we'll presuppose that the set elements are written in the increasing order.
We'll say that the secret is safe if the following conditions are hold:
* for any two indexes i, j (1 β€ i < j β€ k) the intersection of sets Ui and Uj is an empty set;
* the union of sets U1, U2, ..., Uk is set (1, 2, ..., n);
* in each set Ui, its elements ui, 1, ui, 2, ..., ui, |Ui| do not form an arithmetic progression (in particular, |Ui| β₯ 3 should hold).
Let us remind you that the elements of set (u1, u2, ..., us) form an arithmetic progression if there is such number d, that for all i (1 β€ i < s) fulfills ui + d = ui + 1. For example, the elements of sets (5), (1, 10) and (1, 5, 9) form arithmetic progressions and the elements of sets (1, 2, 4) and (3, 6, 8) don't.
Your task is to find any partition of the set of words into subsets U1, U2, ..., Uk so that the secret is safe. Otherwise indicate that there's no such partition.
Input
The input consists of a single line which contains two integers n and k (2 β€ k β€ n β€ 106) β the number of words in the secret and the number of the Keepers. The numbers are separated by a single space.
Output
If there is no way to keep the secret safe, print a single integer "-1" (without the quotes). Otherwise, print n integers, the i-th of them representing the number of the Keeper who's got the i-th word of the secret.
If there are multiple solutions, print any of them.
Examples
Input
11 3
Output
3 1 2 1 1 2 3 2 2 3 1
Input
5 2
Output
-1
Submitted Solution:
```
n, k = map(int, input().split())
if n < 3*k:
print(-1)
quit()
ans = [1]*n
from random import randint
for i in range(n):
ans[i] = randint(1, k)
print(" ".join(str(k) for k in ans))
``` | instruction | 0 | 98,942 | 5 | 197,884 |
No | output | 1 | 98,942 | 5 | 197,885 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Greatest Secret Ever consists of n words, indexed by positive integers from 1 to n. The secret needs dividing between k Keepers (let's index them by positive integers from 1 to k), the i-th Keeper gets a non-empty set of words with numbers from the set Ui = (ui, 1, ui, 2, ..., ui, |Ui|). Here and below we'll presuppose that the set elements are written in the increasing order.
We'll say that the secret is safe if the following conditions are hold:
* for any two indexes i, j (1 β€ i < j β€ k) the intersection of sets Ui and Uj is an empty set;
* the union of sets U1, U2, ..., Uk is set (1, 2, ..., n);
* in each set Ui, its elements ui, 1, ui, 2, ..., ui, |Ui| do not form an arithmetic progression (in particular, |Ui| β₯ 3 should hold).
Let us remind you that the elements of set (u1, u2, ..., us) form an arithmetic progression if there is such number d, that for all i (1 β€ i < s) fulfills ui + d = ui + 1. For example, the elements of sets (5), (1, 10) and (1, 5, 9) form arithmetic progressions and the elements of sets (1, 2, 4) and (3, 6, 8) don't.
Your task is to find any partition of the set of words into subsets U1, U2, ..., Uk so that the secret is safe. Otherwise indicate that there's no such partition.
Input
The input consists of a single line which contains two integers n and k (2 β€ k β€ n β€ 106) β the number of words in the secret and the number of the Keepers. The numbers are separated by a single space.
Output
If there is no way to keep the secret safe, print a single integer "-1" (without the quotes). Otherwise, print n integers, the i-th of them representing the number of the Keeper who's got the i-th word of the secret.
If there are multiple solutions, print any of them.
Examples
Input
11 3
Output
3 1 2 1 1 2 3 2 2 3 1
Input
5 2
Output
-1
Submitted Solution:
```
n, k = map(int, input().split())
if k * 3 < 9:
print(-1)
else:
ans = []
for i in range(1, k * 2 + 1):
ans.append(k if i % k == 0 else i % k)
if k % 2:
ans.append(k)
for i in range(k - 1, 0, -1):
if i % 2:
ans.append(ans[-1] + i)
else:
ans.append(ans[-1] - i)
else:
ans.extend([i for i in range(k, 0, -1)])
ans.extend([(k - (i % k)) for i in range(k * 3 + 1, n + 1)])
print(*ans)
``` | instruction | 0 | 98,943 | 5 | 197,886 |
No | output | 1 | 98,943 | 5 | 197,887 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let us call a pair of integer numbers m-perfect, if at least one number in the pair is greater than or equal to m. Thus, the pairs (3, 3) and (0, 2) are 2-perfect while the pair (-1, 1) is not.
Two integers x, y are written on the blackboard. It is allowed to erase one of them and replace it with the sum of the numbers, (x + y).
What is the minimum number of such operations one has to perform in order to make the given pair of integers m-perfect?
Input
Single line of the input contains three integers x, y and m ( - 1018 β€ x, y, m β€ 1018).
Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preffered to use the cin, cout streams or the %I64d specifier.
Output
Print the minimum number of operations or "-1" (without quotes), if it is impossible to transform the given pair to the m-perfect one.
Examples
Input
1 2 5
Output
2
Input
-1 4 15
Output
4
Input
0 -1 5
Output
-1
Note
In the first sample the following sequence of operations is suitable: (1, 2) <image> (3, 2) <image> (5, 2).
In the second sample: (-1, 4) <image> (3, 4) <image> (7, 4) <image> (11, 4) <image> (15, 4).
Finally, in the third sample x, y cannot be made positive, hence there is no proper sequence of operations.
Submitted Solution:
```
x, y, m = map(int, input().split())
a, b = max(x, y), min(x, y)
if a >= m:
print(0)
exit()
if a <= 0:
print(-1)
exit()
res = 0
if b < 0:
res += -b // a
b += res * a
if a < b:
a, b = b, a
while a < m:
b += a
res += 1
if a < b:
a, b = b, a
print(res)
``` | instruction | 0 | 98,952 | 5 | 197,904 |
Yes | output | 1 | 98,952 | 5 | 197,905 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let us call a pair of integer numbers m-perfect, if at least one number in the pair is greater than or equal to m. Thus, the pairs (3, 3) and (0, 2) are 2-perfect while the pair (-1, 1) is not.
Two integers x, y are written on the blackboard. It is allowed to erase one of them and replace it with the sum of the numbers, (x + y).
What is the minimum number of such operations one has to perform in order to make the given pair of integers m-perfect?
Input
Single line of the input contains three integers x, y and m ( - 1018 β€ x, y, m β€ 1018).
Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preffered to use the cin, cout streams or the %I64d specifier.
Output
Print the minimum number of operations or "-1" (without quotes), if it is impossible to transform the given pair to the m-perfect one.
Examples
Input
1 2 5
Output
2
Input
-1 4 15
Output
4
Input
0 -1 5
Output
-1
Note
In the first sample the following sequence of operations is suitable: (1, 2) <image> (3, 2) <image> (5, 2).
In the second sample: (-1, 4) <image> (3, 4) <image> (7, 4) <image> (11, 4) <image> (15, 4).
Finally, in the third sample x, y cannot be made positive, hence there is no proper sequence of operations.
Submitted Solution:
```
s = input().split()
x, y, m = (int(i) for i in s)
ans = 0
if x >= m or y >= m:
print(0)
elif x <= 0 and y <= 0:
print(-1)
else:
if x < 0:
q = abs(x // y)
ans += q
x += y * q
elif y < 0:
q = abs(y // x)
ans += q
y += x * q
while x < m and y < m:
ans += 1
if x < y:
x = x + y
else:
y = x + y
print(ans)
``` | instruction | 0 | 98,953 | 5 | 197,906 |
Yes | output | 1 | 98,953 | 5 | 197,907 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let us call a pair of integer numbers m-perfect, if at least one number in the pair is greater than or equal to m. Thus, the pairs (3, 3) and (0, 2) are 2-perfect while the pair (-1, 1) is not.
Two integers x, y are written on the blackboard. It is allowed to erase one of them and replace it with the sum of the numbers, (x + y).
What is the minimum number of such operations one has to perform in order to make the given pair of integers m-perfect?
Input
Single line of the input contains three integers x, y and m ( - 1018 β€ x, y, m β€ 1018).
Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preffered to use the cin, cout streams or the %I64d specifier.
Output
Print the minimum number of operations or "-1" (without quotes), if it is impossible to transform the given pair to the m-perfect one.
Examples
Input
1 2 5
Output
2
Input
-1 4 15
Output
4
Input
0 -1 5
Output
-1
Note
In the first sample the following sequence of operations is suitable: (1, 2) <image> (3, 2) <image> (5, 2).
In the second sample: (-1, 4) <image> (3, 4) <image> (7, 4) <image> (11, 4) <image> (15, 4).
Finally, in the third sample x, y cannot be made positive, hence there is no proper sequence of operations.
Submitted Solution:
```
x, y, m = map(int, input().split())
res = 0
if (max(x, y) >= m): print(0)
elif (x+y<m and x<=0 and y<=0):
if (max(x,y)<m): print(-1)
else: print(0)
else:
if x*y<0:
x, y = min(x,y), max(x,y)
if (y>=m):
print(0)
else:
res += -x//y
x += y*res
while(max(x,y)<m):
x, y = max(x,y), x+y
res += 1
print(res)
``` | instruction | 0 | 98,954 | 5 | 197,908 |
Yes | output | 1 | 98,954 | 5 | 197,909 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let us call a pair of integer numbers m-perfect, if at least one number in the pair is greater than or equal to m. Thus, the pairs (3, 3) and (0, 2) are 2-perfect while the pair (-1, 1) is not.
Two integers x, y are written on the blackboard. It is allowed to erase one of them and replace it with the sum of the numbers, (x + y).
What is the minimum number of such operations one has to perform in order to make the given pair of integers m-perfect?
Input
Single line of the input contains three integers x, y and m ( - 1018 β€ x, y, m β€ 1018).
Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preffered to use the cin, cout streams or the %I64d specifier.
Output
Print the minimum number of operations or "-1" (without quotes), if it is impossible to transform the given pair to the m-perfect one.
Examples
Input
1 2 5
Output
2
Input
-1 4 15
Output
4
Input
0 -1 5
Output
-1
Note
In the first sample the following sequence of operations is suitable: (1, 2) <image> (3, 2) <image> (5, 2).
In the second sample: (-1, 4) <image> (3, 4) <image> (7, 4) <image> (11, 4) <image> (15, 4).
Finally, in the third sample x, y cannot be made positive, hence there is no proper sequence of operations.
Submitted Solution:
```
x,y,m=[int(i) for i in input().split(' ')]
x,y=max(x,y), min(x,y)
a=0
if x>=m:print(0); quit()
if x<=0: print(-1); quit()
if x+y<0: a=abs(y//x)+1; y+=a*x
while max(x,y)<m:
if x<y:
x+=y
else:
y+=x
a+=1
print(a)
``` | instruction | 0 | 98,955 | 5 | 197,910 |
Yes | output | 1 | 98,955 | 5 | 197,911 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let us call a pair of integer numbers m-perfect, if at least one number in the pair is greater than or equal to m. Thus, the pairs (3, 3) and (0, 2) are 2-perfect while the pair (-1, 1) is not.
Two integers x, y are written on the blackboard. It is allowed to erase one of them and replace it with the sum of the numbers, (x + y).
What is the minimum number of such operations one has to perform in order to make the given pair of integers m-perfect?
Input
Single line of the input contains three integers x, y and m ( - 1018 β€ x, y, m β€ 1018).
Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preffered to use the cin, cout streams or the %I64d specifier.
Output
Print the minimum number of operations or "-1" (without quotes), if it is impossible to transform the given pair to the m-perfect one.
Examples
Input
1 2 5
Output
2
Input
-1 4 15
Output
4
Input
0 -1 5
Output
-1
Note
In the first sample the following sequence of operations is suitable: (1, 2) <image> (3, 2) <image> (5, 2).
In the second sample: (-1, 4) <image> (3, 4) <image> (7, 4) <image> (11, 4) <image> (15, 4).
Finally, in the third sample x, y cannot be made positive, hence there is no proper sequence of operations.
Submitted Solution:
```
x,y,m=[int(i) for i in input().split(' ')]
x,y=max(x,y), min(x,y)
print(x, y, m)
a=0
if x>=m:print(0); quit()
if x<=0: print(-1); quit()
if x+y<0: a=abs(y//x)+1; y+=a*x
while max(x,y)<m:
if x<y:
x+=y
else:
y+=x
a+=1
print(a)
``` | instruction | 0 | 98,956 | 5 | 197,912 |
No | output | 1 | 98,956 | 5 | 197,913 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let us call a pair of integer numbers m-perfect, if at least one number in the pair is greater than or equal to m. Thus, the pairs (3, 3) and (0, 2) are 2-perfect while the pair (-1, 1) is not.
Two integers x, y are written on the blackboard. It is allowed to erase one of them and replace it with the sum of the numbers, (x + y).
What is the minimum number of such operations one has to perform in order to make the given pair of integers m-perfect?
Input
Single line of the input contains three integers x, y and m ( - 1018 β€ x, y, m β€ 1018).
Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preffered to use the cin, cout streams or the %I64d specifier.
Output
Print the minimum number of operations or "-1" (without quotes), if it is impossible to transform the given pair to the m-perfect one.
Examples
Input
1 2 5
Output
2
Input
-1 4 15
Output
4
Input
0 -1 5
Output
-1
Note
In the first sample the following sequence of operations is suitable: (1, 2) <image> (3, 2) <image> (5, 2).
In the second sample: (-1, 4) <image> (3, 4) <image> (7, 4) <image> (11, 4) <image> (15, 4).
Finally, in the third sample x, y cannot be made positive, hence there is no proper sequence of operations.
Submitted Solution:
```
import math
x,y,m=map(int,input().split())
c=0
x,y=min(x,y),max(x,y)
#print(x,y)
if(y>=m):
print(0)
exit()
elif(x<=0 and y<=0):
print("-1")
exit()
elif(x<0 and y>0):
c+=math.ceil((-1*x)/y)
x+=y*(math.ceil((-1*x)/y))
#print(x,y,c)
if x+y>=m:
print(c+1)
else:
if x==0:
x+=y
y+=y
c+=2
print(c+math.ceil((m+x)/(x+y)))
``` | instruction | 0 | 98,957 | 5 | 197,914 |
No | output | 1 | 98,957 | 5 | 197,915 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let us call a pair of integer numbers m-perfect, if at least one number in the pair is greater than or equal to m. Thus, the pairs (3, 3) and (0, 2) are 2-perfect while the pair (-1, 1) is not.
Two integers x, y are written on the blackboard. It is allowed to erase one of them and replace it with the sum of the numbers, (x + y).
What is the minimum number of such operations one has to perform in order to make the given pair of integers m-perfect?
Input
Single line of the input contains three integers x, y and m ( - 1018 β€ x, y, m β€ 1018).
Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preffered to use the cin, cout streams or the %I64d specifier.
Output
Print the minimum number of operations or "-1" (without quotes), if it is impossible to transform the given pair to the m-perfect one.
Examples
Input
1 2 5
Output
2
Input
-1 4 15
Output
4
Input
0 -1 5
Output
-1
Note
In the first sample the following sequence of operations is suitable: (1, 2) <image> (3, 2) <image> (5, 2).
In the second sample: (-1, 4) <image> (3, 4) <image> (7, 4) <image> (11, 4) <image> (15, 4).
Finally, in the third sample x, y cannot be made positive, hence there is no proper sequence of operations.
Submitted Solution:
```
x,y,m = map(int,input().split())
a=max(x,y)
if a<=0 and m>a:
print(-1)
else:
b=max(x,y)
a=min(x,y)
ans = abs(b-a)//b
a+=(b-a)*ans
while max(a,b)<m:
if a<=b:
a=a+b
else:
b=a+b
ans+=1
print(ans)
``` | instruction | 0 | 98,958 | 5 | 197,916 |
No | output | 1 | 98,958 | 5 | 197,917 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let us call a pair of integer numbers m-perfect, if at least one number in the pair is greater than or equal to m. Thus, the pairs (3, 3) and (0, 2) are 2-perfect while the pair (-1, 1) is not.
Two integers x, y are written on the blackboard. It is allowed to erase one of them and replace it with the sum of the numbers, (x + y).
What is the minimum number of such operations one has to perform in order to make the given pair of integers m-perfect?
Input
Single line of the input contains three integers x, y and m ( - 1018 β€ x, y, m β€ 1018).
Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preffered to use the cin, cout streams or the %I64d specifier.
Output
Print the minimum number of operations or "-1" (without quotes), if it is impossible to transform the given pair to the m-perfect one.
Examples
Input
1 2 5
Output
2
Input
-1 4 15
Output
4
Input
0 -1 5
Output
-1
Note
In the first sample the following sequence of operations is suitable: (1, 2) <image> (3, 2) <image> (5, 2).
In the second sample: (-1, 4) <image> (3, 4) <image> (7, 4) <image> (11, 4) <image> (15, 4).
Finally, in the third sample x, y cannot be made positive, hence there is no proper sequence of operations.
Submitted Solution:
```
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")
from collections import defaultdict
from math import ceil,floor,sqrt,log2,gcd
from heapq import heappush,heappop
from bisect import bisect_left,bisect
import sys
abc='abcdefghijklmnopqrstuvwxyz'
a,b,x=map(int,input().split())
c=0
if a>=x or b>=x:
print(0)
elif (a+b)<=0:
print(-1)
else:
while a<x and b<x:
# print(a,b)
if a<b:
a+=b
c+=1
else:
b+=a
c+=1
# print(a,b)
print(c)
``` | instruction | 0 | 98,959 | 5 | 197,918 |
No | output | 1 | 98,959 | 5 | 197,919 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
At the children's day, the child came to Picks's house, and messed his house up. Picks was angry at him. A lot of important things were lost, in particular the favorite set of Picks.
Fortunately, Picks remembers something about his set S:
* its elements were distinct integers from 1 to limit;
* the value of <image> was equal to sum; here lowbit(x) equals 2k where k is the position of the first one in the binary representation of x. For example, lowbit(100102) = 102, lowbit(100012) = 12, lowbit(100002) = 100002 (binary representation).
Can you help Picks and find any set S, that satisfies all the above conditions?
Input
The first line contains two integers: sum, limit (1 β€ sum, limit β€ 105).
Output
In the first line print an integer n (1 β€ n β€ 105), denoting the size of S. Then print the elements of set S in any order. If there are multiple answers, print any of them.
If it's impossible to find a suitable set, print -1.
Examples
Input
5 5
Output
2
4 5
Input
4 3
Output
3
2 3 1
Input
5 1
Output
-1
Note
In sample test 1: lowbit(4) = 4, lowbit(5) = 1, 4 + 1 = 5.
In sample test 2: lowbit(1) = 1, lowbit(2) = 2, lowbit(3) = 1, 1 + 2 + 1 = 4.
Submitted Solution:
```
def check(num):
x=str(bin(num))
j=-1
for i in range(len(x)-1,-1,-1):
j+=1
if(x[i]=='1'):
break
return j
s,limit=[int(x) for x in input().split()]
res=[]
for i in range(1,limit+1):
x=check(i)
res.append([2**x,i])
res.sort(key=lambda x:x[0])
#print(res)
ans=[]
for i in range(len(res)-1,-1,-1):
if(s>=res[i][0]):
s-=res[i][0]
ans.append(res[i][1])
if(s==0):
break
if(s!=0):
print(-1)
else:
print(len(ans))
print(*ans,sep=" ")
``` | instruction | 0 | 99,014 | 5 | 198,028 |
Yes | output | 1 | 99,014 | 5 | 198,029 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
At the children's day, the child came to Picks's house, and messed his house up. Picks was angry at him. A lot of important things were lost, in particular the favorite set of Picks.
Fortunately, Picks remembers something about his set S:
* its elements were distinct integers from 1 to limit;
* the value of <image> was equal to sum; here lowbit(x) equals 2k where k is the position of the first one in the binary representation of x. For example, lowbit(100102) = 102, lowbit(100012) = 12, lowbit(100002) = 100002 (binary representation).
Can you help Picks and find any set S, that satisfies all the above conditions?
Input
The first line contains two integers: sum, limit (1 β€ sum, limit β€ 105).
Output
In the first line print an integer n (1 β€ n β€ 105), denoting the size of S. Then print the elements of set S in any order. If there are multiple answers, print any of them.
If it's impossible to find a suitable set, print -1.
Examples
Input
5 5
Output
2
4 5
Input
4 3
Output
3
2 3 1
Input
5 1
Output
-1
Note
In sample test 1: lowbit(4) = 4, lowbit(5) = 1, 4 + 1 = 5.
In sample test 2: lowbit(1) = 1, lowbit(2) = 2, lowbit(3) = 1, 1 + 2 + 1 = 4.
Submitted Solution:
```
n, m = map(int, input().split())
vals = {}
temp = []
for j in range(1, m + 1):
lowest_bit = j & (-j)
if lowest_bit not in vals:
vals[lowest_bit] = []
vals[lowest_bit].append(j)
temp.append(lowest_bit)
temp.sort()
result = []
for x in reversed(temp):
if x <=n and len(vals[x]):
n -= x
result.append(vals[x][-1])
vals[x].pop()
if n == 0:
print(len(result))
print(*result)
else:
print(-1)
``` | instruction | 0 | 99,015 | 5 | 198,030 |
Yes | output | 1 | 99,015 | 5 | 198,031 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
At the children's day, the child came to Picks's house, and messed his house up. Picks was angry at him. A lot of important things were lost, in particular the favorite set of Picks.
Fortunately, Picks remembers something about his set S:
* its elements were distinct integers from 1 to limit;
* the value of <image> was equal to sum; here lowbit(x) equals 2k where k is the position of the first one in the binary representation of x. For example, lowbit(100102) = 102, lowbit(100012) = 12, lowbit(100002) = 100002 (binary representation).
Can you help Picks and find any set S, that satisfies all the above conditions?
Input
The first line contains two integers: sum, limit (1 β€ sum, limit β€ 105).
Output
In the first line print an integer n (1 β€ n β€ 105), denoting the size of S. Then print the elements of set S in any order. If there are multiple answers, print any of them.
If it's impossible to find a suitable set, print -1.
Examples
Input
5 5
Output
2
4 5
Input
4 3
Output
3
2 3 1
Input
5 1
Output
-1
Note
In sample test 1: lowbit(4) = 4, lowbit(5) = 1, 4 + 1 = 5.
In sample test 2: lowbit(1) = 1, lowbit(2) = 2, lowbit(3) = 1, 1 + 2 + 1 = 4.
Submitted Solution:
```
s,limit=map(int,input().split())
Cnt=[[]]
for i in range(10**5):
Cnt.append([])
Ind=[0]*(10**5+1)
m=0
for i in range(1,limit+1):
pos=0
x=i
while(x%2==0):
x//=2
pos+=1
Cnt[2**pos].append(i)
m=max(m,2**pos)
L=[]
while(s>0):
e=s
for j in range(min(m,s),-1,-1):
if(Ind[j]<len(Cnt[j])):
L.append(Cnt[j][Ind[j]])
Ind[j]+=1
s-=j
m=min(m,j)
break
if(s==e):
print(-1)
break
if(s==0):
print(len(L))
for item in L:
print(item,end=" ")
``` | instruction | 0 | 99,016 | 5 | 198,032 |
Yes | output | 1 | 99,016 | 5 | 198,033 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
At the children's day, the child came to Picks's house, and messed his house up. Picks was angry at him. A lot of important things were lost, in particular the favorite set of Picks.
Fortunately, Picks remembers something about his set S:
* its elements were distinct integers from 1 to limit;
* the value of <image> was equal to sum; here lowbit(x) equals 2k where k is the position of the first one in the binary representation of x. For example, lowbit(100102) = 102, lowbit(100012) = 12, lowbit(100002) = 100002 (binary representation).
Can you help Picks and find any set S, that satisfies all the above conditions?
Input
The first line contains two integers: sum, limit (1 β€ sum, limit β€ 105).
Output
In the first line print an integer n (1 β€ n β€ 105), denoting the size of S. Then print the elements of set S in any order. If there are multiple answers, print any of them.
If it's impossible to find a suitable set, print -1.
Examples
Input
5 5
Output
2
4 5
Input
4 3
Output
3
2 3 1
Input
5 1
Output
-1
Note
In sample test 1: lowbit(4) = 4, lowbit(5) = 1, 4 + 1 = 5.
In sample test 2: lowbit(1) = 1, lowbit(2) = 2, lowbit(3) = 1, 1 + 2 + 1 = 4.
Submitted Solution:
```
n,m=map(int,input().split())
ans=[]
maxa=0
count=0
from collections import defaultdict
al=defaultdict(list)
for i in range(1,m+1):
temp=bin(i)
temp=temp[2:]
temp=temp[::-1]
flag=0
for j in range(len(temp)):
if(temp[j]=='1'):
al[pow(2,j)].append(i)
count+=pow(2,j)
maxa=max(maxa,pow(2,j))
flag=1
if(flag==1):
break;
ans=[]
if(n>count):
print(-1)
else:
while(maxa>=1 and n>0):
if(n>=maxa):
index=len(al[maxa])-1
while(n>=maxa and len(al[maxa])>0):
ans.append(al[maxa][index])
n-=maxa
al[maxa].pop()
index-=1
maxa=maxa//2
print(len(ans))
print(*ans)
``` | instruction | 0 | 99,017 | 5 | 198,034 |
Yes | output | 1 | 99,017 | 5 | 198,035 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
At the children's day, the child came to Picks's house, and messed his house up. Picks was angry at him. A lot of important things were lost, in particular the favorite set of Picks.
Fortunately, Picks remembers something about his set S:
* its elements were distinct integers from 1 to limit;
* the value of <image> was equal to sum; here lowbit(x) equals 2k where k is the position of the first one in the binary representation of x. For example, lowbit(100102) = 102, lowbit(100012) = 12, lowbit(100002) = 100002 (binary representation).
Can you help Picks and find any set S, that satisfies all the above conditions?
Input
The first line contains two integers: sum, limit (1 β€ sum, limit β€ 105).
Output
In the first line print an integer n (1 β€ n β€ 105), denoting the size of S. Then print the elements of set S in any order. If there are multiple answers, print any of them.
If it's impossible to find a suitable set, print -1.
Examples
Input
5 5
Output
2
4 5
Input
4 3
Output
3
2 3 1
Input
5 1
Output
-1
Note
In sample test 1: lowbit(4) = 4, lowbit(5) = 1, 4 + 1 = 5.
In sample test 2: lowbit(1) = 1, lowbit(2) = 2, lowbit(3) = 1, 1 + 2 + 1 = 4.
Submitted Solution:
```
def lowbit(x):
c = 1
while x:
if x % 2:
return c
c *= 2
x /= 2
s, l = map(int, input().split())
x = []
for i in range(1, l + 1):
x.append(lowbit(i))
ss = sum(x)
if ss < s: print(-1)
else:
xx = 0; res = []; rc = 0
for i in range(len(x)):
if xx + x[i] <= s:
xx += x[i]
res.append(i + 1)
rc += 1
if xx == s:
print(rc)
for i in range(rc):
print(res[i], end=' ')
else:
print(-1)
``` | instruction | 0 | 99,018 | 5 | 198,036 |
No | output | 1 | 99,018 | 5 | 198,037 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
At the children's day, the child came to Picks's house, and messed his house up. Picks was angry at him. A lot of important things were lost, in particular the favorite set of Picks.
Fortunately, Picks remembers something about his set S:
* its elements were distinct integers from 1 to limit;
* the value of <image> was equal to sum; here lowbit(x) equals 2k where k is the position of the first one in the binary representation of x. For example, lowbit(100102) = 102, lowbit(100012) = 12, lowbit(100002) = 100002 (binary representation).
Can you help Picks and find any set S, that satisfies all the above conditions?
Input
The first line contains two integers: sum, limit (1 β€ sum, limit β€ 105).
Output
In the first line print an integer n (1 β€ n β€ 105), denoting the size of S. Then print the elements of set S in any order. If there are multiple answers, print any of them.
If it's impossible to find a suitable set, print -1.
Examples
Input
5 5
Output
2
4 5
Input
4 3
Output
3
2 3 1
Input
5 1
Output
-1
Note
In sample test 1: lowbit(4) = 4, lowbit(5) = 1, 4 + 1 = 5.
In sample test 2: lowbit(1) = 1, lowbit(2) = 2, lowbit(3) = 1, 1 + 2 + 1 = 4.
Submitted Solution:
```
sum,limit = map(int,input().split())
def lowbit(k):
count = 0
for i in k[::-1]:
if i == '1':
return 2**count
else:
count+=1
actual = 0
for i in range(1,limit+1):
c = bin(i)[2:]
actual+=lowbit(c)
# print(actual)
if sum<=actual:
ans = []
count = 0
for i in range(2,limit+1,2):
count+=lowbit(bin(i)[2:])
# print(count)
ans.append(i)
if count > sum:
count-=lowbit(bin(i)[2:])
ans.pop(-1)
break
for i in range(1,limit+1,2):
if count == sum:
break
else:
count+=lowbit(bin(i)[2:])
ans.append(i)
print(len(ans))
print(*ans)
else:
print(-1)
``` | instruction | 0 | 99,019 | 5 | 198,038 |
No | output | 1 | 99,019 | 5 | 198,039 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
At the children's day, the child came to Picks's house, and messed his house up. Picks was angry at him. A lot of important things were lost, in particular the favorite set of Picks.
Fortunately, Picks remembers something about his set S:
* its elements were distinct integers from 1 to limit;
* the value of <image> was equal to sum; here lowbit(x) equals 2k where k is the position of the first one in the binary representation of x. For example, lowbit(100102) = 102, lowbit(100012) = 12, lowbit(100002) = 100002 (binary representation).
Can you help Picks and find any set S, that satisfies all the above conditions?
Input
The first line contains two integers: sum, limit (1 β€ sum, limit β€ 105).
Output
In the first line print an integer n (1 β€ n β€ 105), denoting the size of S. Then print the elements of set S in any order. If there are multiple answers, print any of them.
If it's impossible to find a suitable set, print -1.
Examples
Input
5 5
Output
2
4 5
Input
4 3
Output
3
2 3 1
Input
5 1
Output
-1
Note
In sample test 1: lowbit(4) = 4, lowbit(5) = 1, 4 + 1 = 5.
In sample test 2: lowbit(1) = 1, lowbit(2) = 2, lowbit(3) = 1, 1 + 2 + 1 = 4.
Submitted Solution:
```
s,l=map(int,input().split())
list1=[]
for i in range(1,l+1):
list1.append(i&-i)
list1.sort(reverse=True)
ll=[]
for i in range(l):
if(list1[i]<=s):
ll.append(list1[i])
s-=list1[i]
if(s==0):
print(len(ll))
print(*ll)
else:
print(-1)
``` | instruction | 0 | 99,020 | 5 | 198,040 |
No | output | 1 | 99,020 | 5 | 198,041 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
At the children's day, the child came to Picks's house, and messed his house up. Picks was angry at him. A lot of important things were lost, in particular the favorite set of Picks.
Fortunately, Picks remembers something about his set S:
* its elements were distinct integers from 1 to limit;
* the value of <image> was equal to sum; here lowbit(x) equals 2k where k is the position of the first one in the binary representation of x. For example, lowbit(100102) = 102, lowbit(100012) = 12, lowbit(100002) = 100002 (binary representation).
Can you help Picks and find any set S, that satisfies all the above conditions?
Input
The first line contains two integers: sum, limit (1 β€ sum, limit β€ 105).
Output
In the first line print an integer n (1 β€ n β€ 105), denoting the size of S. Then print the elements of set S in any order. If there are multiple answers, print any of them.
If it's impossible to find a suitable set, print -1.
Examples
Input
5 5
Output
2
4 5
Input
4 3
Output
3
2 3 1
Input
5 1
Output
-1
Note
In sample test 1: lowbit(4) = 4, lowbit(5) = 1, 4 + 1 = 5.
In sample test 2: lowbit(1) = 1, lowbit(2) = 2, lowbit(3) = 1, 1 + 2 + 1 = 4.
Submitted Solution:
```
sum, limit = map (int, input().split())
x = 0
lis = list()
for i in range (sum, 0, -1) :
if limit > 0 and x < sum :
if i % 2 == 0 and i % 4 != 0 :
x += 2
lis.append (i)
limit -= 1
elif i % 4 == 0 :
x += i
lis.append (i)
limit -= 1
else :
x += 1
lis.append (i)
limit -= 1
if x != sum :
print (-1)
else :
print (len (lis))
for i in lis :
print (i, "", end = '')
``` | instruction | 0 | 99,021 | 5 | 198,042 |
No | output | 1 | 99,021 | 5 | 198,043 |
Provide a correct Python 3 solution for this coding contest problem.
Enter a positive integer n of 4,000 or less, with a pair of integers a, b, c, d in the range 0-1000.
a + b + c + d = n
Create a program that outputs the number of combinations that satisfy the conditions.
Input
Given multiple datasets. Each dataset is given n on one row. Please process until the end of the input.
The number of datasets does not exceed 50.
Output
For each data set, output the number of combinations of a, b, c, and d on one line.
Example
Input
2
3
35
Output
10
20
8436 | instruction | 0 | 99,345 | 5 | 198,690 |
"Correct Solution:
```
import sys
m=1000;n=m*4
a=[0]*-~n
for i in range(2001):a[i]=a[n-i]=(i+3)*(i+2)*(i+1)//6-a[~-i-m]*4*(i>~-m)
for e in sys.stdin:print(a[int(e)])
``` | output | 1 | 99,345 | 5 | 198,691 |
Provide a correct Python 3 solution for this coding contest problem.
Enter a positive integer n of 4,000 or less, with a pair of integers a, b, c, d in the range 0-1000.
a + b + c + d = n
Create a program that outputs the number of combinations that satisfy the conditions.
Input
Given multiple datasets. Each dataset is given n on one row. Please process until the end of the input.
The number of datasets does not exceed 50.
Output
For each data set, output the number of combinations of a, b, c, and d on one line.
Example
Input
2
3
35
Output
10
20
8436 | instruction | 0 | 99,346 | 5 | 198,692 |
"Correct Solution:
```
while True:
try:
n = int(input())
if n > 2000:
n = 4000 - n
ans = (n+1)*(n+2)*(n+3)/6
if n >= 1001:
n = n - 1001
ans = ans - 2*(n+1)*(n+2)*(n+3)/3
print(int(ans))
except EOFError:
break
``` | output | 1 | 99,346 | 5 | 198,693 |
Provide a correct Python 3 solution for this coding contest problem.
Enter a positive integer n of 4,000 or less, with a pair of integers a, b, c, d in the range 0-1000.
a + b + c + d = n
Create a program that outputs the number of combinations that satisfy the conditions.
Input
Given multiple datasets. Each dataset is given n on one row. Please process until the end of the input.
The number of datasets does not exceed 50.
Output
For each data set, output the number of combinations of a, b, c, and d on one line.
Example
Input
2
3
35
Output
10
20
8436 | instruction | 0 | 99,347 | 5 | 198,694 |
"Correct Solution:
```
import sys
a=[0]*4001
for i in range(1999):a[i]=a[4000-i]=(i+3)*(i+2)*(i+1)//6-a[i-1001]*4*(i>999)
for e in sys.stdin:print(a[int(e)])
``` | output | 1 | 99,347 | 5 | 198,695 |
Provide a correct Python 3 solution for this coding contest problem.
Enter a positive integer n of 4,000 or less, with a pair of integers a, b, c, d in the range 0-1000.
a + b + c + d = n
Create a program that outputs the number of combinations that satisfy the conditions.
Input
Given multiple datasets. Each dataset is given n on one row. Please process until the end of the input.
The number of datasets does not exceed 50.
Output
For each data set, output the number of combinations of a, b, c, and d on one line.
Example
Input
2
3
35
Output
10
20
8436 | instruction | 0 | 99,348 | 5 | 198,696 |
"Correct Solution:
```
# -*- coding: utf-8 -*-
import sys
import os
import math
T = [0] * 2001
for a in range(1001):
for b in range(1001):
T[a + b] += 1
for s in sys.stdin:
n = int(s)
sum_n_num = 0
for a_b_sum in range(0, n+1):
c_d_sum = n - a_b_sum
if a_b_sum <= 2000 and c_d_sum <= 2000:
sum_n_num += T[a_b_sum] * T[c_d_sum]
print(sum_n_num)
``` | output | 1 | 99,348 | 5 | 198,697 |
Provide a correct Python 3 solution for this coding contest problem.
Enter a positive integer n of 4,000 or less, with a pair of integers a, b, c, d in the range 0-1000.
a + b + c + d = n
Create a program that outputs the number of combinations that satisfy the conditions.
Input
Given multiple datasets. Each dataset is given n on one row. Please process until the end of the input.
The number of datasets does not exceed 50.
Output
For each data set, output the number of combinations of a, b, c, and d on one line.
Example
Input
2
3
35
Output
10
20
8436 | instruction | 0 | 99,349 | 5 | 198,698 |
"Correct Solution:
```
A = [0 for i in range(2001)]
for i in range(1001) :
for j in range(1001) :
A[i + j] += 1
while True :
try :
n = int(input())
cnt = 0
if(n > 4000) :
print(0)
elif(n > 2000) :
for i in range(n - 2000, 2001) :
cnt += A[i] * A[n - i]
print(cnt)
else :
for i in range(n + 1) :
cnt += A[i] * A[n - i]
print(cnt)
except :
break
``` | output | 1 | 99,349 | 5 | 198,699 |
Provide a correct Python 3 solution for this coding contest problem.
Enter a positive integer n of 4,000 or less, with a pair of integers a, b, c, d in the range 0-1000.
a + b + c + d = n
Create a program that outputs the number of combinations that satisfy the conditions.
Input
Given multiple datasets. Each dataset is given n on one row. Please process until the end of the input.
The number of datasets does not exceed 50.
Output
For each data set, output the number of combinations of a, b, c, and d on one line.
Example
Input
2
3
35
Output
10
20
8436 | instruction | 0 | 99,350 | 5 | 198,700 |
"Correct Solution:
```
s = list(range(1,1001)) + list(range(1001,0,-1))
while True:
try:
n = int(input())
except:
break
ans = 0
for i in range(min(n+1,2001)):
if 0 <= n-i <= 2000:
ans += s[i] * s[n-i]
print(ans)
``` | output | 1 | 99,350 | 5 | 198,701 |
Provide a correct Python 3 solution for this coding contest problem.
Enter a positive integer n of 4,000 or less, with a pair of integers a, b, c, d in the range 0-1000.
a + b + c + d = n
Create a program that outputs the number of combinations that satisfy the conditions.
Input
Given multiple datasets. Each dataset is given n on one row. Please process until the end of the input.
The number of datasets does not exceed 50.
Output
For each data set, output the number of combinations of a, b, c, and d on one line.
Example
Input
2
3
35
Output
10
20
8436 | instruction | 0 | 99,351 | 5 | 198,702 |
"Correct Solution:
```
from collections import Counter
pair_dict = Counter()
for i in range(2001):
pair_dict[i] = min(i, 2000 - i) + 1
while True:
try:
n = int(input())
ans = 0
for i in range(n + 1):
ans += pair_dict[i] * pair_dict[n - i]
print(ans)
except EOFError:
break
``` | output | 1 | 99,351 | 5 | 198,703 |
Provide a correct Python 3 solution for this coding contest problem.
Enter a positive integer n of 4,000 or less, with a pair of integers a, b, c, d in the range 0-1000.
a + b + c + d = n
Create a program that outputs the number of combinations that satisfy the conditions.
Input
Given multiple datasets. Each dataset is given n on one row. Please process until the end of the input.
The number of datasets does not exceed 50.
Output
For each data set, output the number of combinations of a, b, c, and d on one line.
Example
Input
2
3
35
Output
10
20
8436 | instruction | 0 | 99,352 | 5 | 198,704 |
"Correct Solution:
```
import sys
for line in sys.stdin.readlines():
n = int(line.rstrip())
count = 0
for i in range(1001):
if 0 <= n - i <= 1000:
count += (n-i+1)*(i+1)
elif 1001 <= n-i <= 2000 :
count += (2000-(n-i)+1)*(i+1)
for i in range(1001,2001):
if 0 <= n - i <= 1000:
count += (n-i+1)*(2000-i+1)
elif 1001 <= n-i <= 2000:
count += (2000-(n-i)+1)*(2000-i+1)
print(count)
``` | output | 1 | 99,352 | 5 | 198,705 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Enter a positive integer n of 4,000 or less, with a pair of integers a, b, c, d in the range 0-1000.
a + b + c + d = n
Create a program that outputs the number of combinations that satisfy the conditions.
Input
Given multiple datasets. Each dataset is given n on one row. Please process until the end of the input.
The number of datasets does not exceed 50.
Output
For each data set, output the number of combinations of a, b, c, and d on one line.
Example
Input
2
3
35
Output
10
20
8436
Submitted Solution:
```
s=[0]*4001
for i in range(2001):
a=a+2*(i-999)*(i-1000) if i>1000 else 0
s[i]=(i+3)*(i+2)*-~i//6-a
s[4000-i]=s[i]
while 1:
try:print(s[int(input())])
except:break
``` | instruction | 0 | 99,355 | 5 | 198,710 |
Yes | output | 1 | 99,355 | 5 | 198,711 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Enter a positive integer n of 4,000 or less, with a pair of integers a, b, c, d in the range 0-1000.
a + b + c + d = n
Create a program that outputs the number of combinations that satisfy the conditions.
Input
Given multiple datasets. Each dataset is given n on one row. Please process until the end of the input.
The number of datasets does not exceed 50.
Output
For each data set, output the number of combinations of a, b, c, and d on one line.
Example
Input
2
3
35
Output
10
20
8436
Submitted Solution:
```
while True:
try:
N = int(input())
except EOFError:
break
ans = (N + 3) * (N + 2) * (N + 1) // 6
print(ans)
``` | instruction | 0 | 99,360 | 5 | 198,720 |
No | output | 1 | 99,360 | 5 | 198,721 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For given integers m and n, compute mn (mod 1,000,000,007). Here, A (mod M) is the remainder when A is divided by M.
Constraints
* 1 β€ m β€ 100
* 1 β€ n β€ 109
Input
m n
Two integers m and n are given in a line.
Output
Print mn (mod 1,000,000,007) in a line.
Examples
Input
2 3
Output
8
Input
5 8
Output
390625
Submitted Solution:
```
m,n=map(int, input().split())
MOD=10**9+7
ans = 1
t = m
while n:
if n&1: ans = (ans*t)%MOD
n >>= 1
t = (t*t)%MOD
print(ans)
``` | instruction | 0 | 99,455 | 5 | 198,910 |
Yes | output | 1 | 99,455 | 5 | 198,911 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Mishka is trying really hard to avoid being kicked out of the university. In particular, he was doing absolutely nothing for the whole semester, miraculously passed some exams so that just one is left.
There were n classes of that subject during the semester and on i-th class professor mentioned some non-negative integer a_i to the students. It turned out, the exam was to tell the whole sequence back to the professor.
Sounds easy enough for those who attended every class, doesn't it?
Obviously Mishka didn't attend any classes. However, professor left some clues on the values of a to help out students like Mishka:
* a was sorted in non-decreasing order (a_1 β€ a_2 β€ ... β€ a_n);
* n was even;
* the following sequence b, consisting of \frac n 2 elements, was formed and given out to students: b_i = a_i + a_{n - i + 1}.
Professor also mentioned that any sequence a, which produces sequence b with the presented technique, will be acceptable.
Help Mishka to pass that last exam. Restore any sorted sequence a of non-negative integers, which produces sequence b with the presented technique. It is guaranteed that there exists at least one correct sequence a, which produces the given sequence b.
Input
The first line contains a single integer n (2 β€ n β€ 2 β
10^5) β the length of sequence a. n is always even.
The second line contains \frac n 2 integers b_1, b_2, ..., b_{\frac n 2} (0 β€ b_i β€ 10^{18}) β sequence b, where b_i = a_i + a_{n - i + 1}.
It is guaranteed that there exists at least one correct sequence a, which produces the given sequence b.
Output
Print n integers a_1, a_2, ..., a_n (0 β€ a_i β€ 10^{18}) in a single line.
a_1 β€ a_2 β€ ... β€ a_n should be satisfied.
b_i = a_i + a_{n - i + 1} should be satisfied for all valid i.
Examples
Input
4
5 6
Output
2 3 3 3
Input
6
2 1 2
Output
0 0 1 1 1 2
Submitted Solution:
```
n = int(input())
b = [int(w) for w in input().split()]
a = [0]*n
l = n//2 - 1
r = n//2
a[l] = b[l] // 2
a[r] = b[l] - a[l]
while l > 0:
if b[l-1] >= b[l]:
a[l-1] = a[l]
a[r+1] = b[l-1] - a[l]
else:
a[r+1] = a[r]
a[l-1] = b[l-1] - a[r]
l -= 1
r += 1
print(*a)
``` | instruction | 0 | 99,511 | 5 | 199,022 |
Yes | output | 1 | 99,511 | 5 | 199,023 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Mishka is trying really hard to avoid being kicked out of the university. In particular, he was doing absolutely nothing for the whole semester, miraculously passed some exams so that just one is left.
There were n classes of that subject during the semester and on i-th class professor mentioned some non-negative integer a_i to the students. It turned out, the exam was to tell the whole sequence back to the professor.
Sounds easy enough for those who attended every class, doesn't it?
Obviously Mishka didn't attend any classes. However, professor left some clues on the values of a to help out students like Mishka:
* a was sorted in non-decreasing order (a_1 β€ a_2 β€ ... β€ a_n);
* n was even;
* the following sequence b, consisting of \frac n 2 elements, was formed and given out to students: b_i = a_i + a_{n - i + 1}.
Professor also mentioned that any sequence a, which produces sequence b with the presented technique, will be acceptable.
Help Mishka to pass that last exam. Restore any sorted sequence a of non-negative integers, which produces sequence b with the presented technique. It is guaranteed that there exists at least one correct sequence a, which produces the given sequence b.
Input
The first line contains a single integer n (2 β€ n β€ 2 β
10^5) β the length of sequence a. n is always even.
The second line contains \frac n 2 integers b_1, b_2, ..., b_{\frac n 2} (0 β€ b_i β€ 10^{18}) β sequence b, where b_i = a_i + a_{n - i + 1}.
It is guaranteed that there exists at least one correct sequence a, which produces the given sequence b.
Output
Print n integers a_1, a_2, ..., a_n (0 β€ a_i β€ 10^{18}) in a single line.
a_1 β€ a_2 β€ ... β€ a_n should be satisfied.
b_i = a_i + a_{n - i + 1} should be satisfied for all valid i.
Examples
Input
4
5 6
Output
2 3 3 3
Input
6
2 1 2
Output
0 0 1 1 1 2
Submitted Solution:
```
n=int(input())
a=[0]*n
b=[int(i) for i in input().split()]
for i in range(n//2):
a[i]=0
a[n-i-1]=b[i]
if(i==0):
continue
adj = max(a[i-1]-a[i],a[n-1-i]-a[n-i])
a[i]+=adj
a[n-i-1]-=adj
print(*a)
``` | instruction | 0 | 99,512 | 5 | 199,024 |
Yes | output | 1 | 99,512 | 5 | 199,025 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Mishka is trying really hard to avoid being kicked out of the university. In particular, he was doing absolutely nothing for the whole semester, miraculously passed some exams so that just one is left.
There were n classes of that subject during the semester and on i-th class professor mentioned some non-negative integer a_i to the students. It turned out, the exam was to tell the whole sequence back to the professor.
Sounds easy enough for those who attended every class, doesn't it?
Obviously Mishka didn't attend any classes. However, professor left some clues on the values of a to help out students like Mishka:
* a was sorted in non-decreasing order (a_1 β€ a_2 β€ ... β€ a_n);
* n was even;
* the following sequence b, consisting of \frac n 2 elements, was formed and given out to students: b_i = a_i + a_{n - i + 1}.
Professor also mentioned that any sequence a, which produces sequence b with the presented technique, will be acceptable.
Help Mishka to pass that last exam. Restore any sorted sequence a of non-negative integers, which produces sequence b with the presented technique. It is guaranteed that there exists at least one correct sequence a, which produces the given sequence b.
Input
The first line contains a single integer n (2 β€ n β€ 2 β
10^5) β the length of sequence a. n is always even.
The second line contains \frac n 2 integers b_1, b_2, ..., b_{\frac n 2} (0 β€ b_i β€ 10^{18}) β sequence b, where b_i = a_i + a_{n - i + 1}.
It is guaranteed that there exists at least one correct sequence a, which produces the given sequence b.
Output
Print n integers a_1, a_2, ..., a_n (0 β€ a_i β€ 10^{18}) in a single line.
a_1 β€ a_2 β€ ... β€ a_n should be satisfied.
b_i = a_i + a_{n - i + 1} should be satisfied for all valid i.
Examples
Input
4
5 6
Output
2 3 3 3
Input
6
2 1 2
Output
0 0 1 1 1 2
Submitted Solution:
```
import re
import sys
exit=sys.exit
from bisect import bisect_left as bsl,bisect_right as bsr
from collections import Counter,defaultdict as ddict,deque
from functools import lru_cache
cache=lru_cache(None)
from heapq import *
from itertools import *
from math import inf
from pprint import pprint as pp
enum=enumerate
ri=lambda:int(rln())
ris=lambda:list(map(int,rfs()))
rln=sys.stdin.readline
rl=lambda:rln().rstrip('\n')
rfs=lambda:rln().split()
cat=''.join
catn='\n'.join
mod=1000000007
d4=[(0,-1),(1,0),(0,1),(-1,0)]
d8=[(-1,-1),(0,-1),(1,-1),(-1,0),(1,0),(-1,1),(0,1),(1,1)]
########################################################################
n=ri()
b=ris()
a=[0]*n
lo,hi=0,inf
for i,x in enum(b):
hi=min(x-lo,hi)
lo=max(lo,x-hi)
a[i],a[~i]=lo,hi
print(*a)
``` | instruction | 0 | 99,513 | 5 | 199,026 |
Yes | output | 1 | 99,513 | 5 | 199,027 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Mishka is trying really hard to avoid being kicked out of the university. In particular, he was doing absolutely nothing for the whole semester, miraculously passed some exams so that just one is left.
There were n classes of that subject during the semester and on i-th class professor mentioned some non-negative integer a_i to the students. It turned out, the exam was to tell the whole sequence back to the professor.
Sounds easy enough for those who attended every class, doesn't it?
Obviously Mishka didn't attend any classes. However, professor left some clues on the values of a to help out students like Mishka:
* a was sorted in non-decreasing order (a_1 β€ a_2 β€ ... β€ a_n);
* n was even;
* the following sequence b, consisting of \frac n 2 elements, was formed and given out to students: b_i = a_i + a_{n - i + 1}.
Professor also mentioned that any sequence a, which produces sequence b with the presented technique, will be acceptable.
Help Mishka to pass that last exam. Restore any sorted sequence a of non-negative integers, which produces sequence b with the presented technique. It is guaranteed that there exists at least one correct sequence a, which produces the given sequence b.
Input
The first line contains a single integer n (2 β€ n β€ 2 β
10^5) β the length of sequence a. n is always even.
The second line contains \frac n 2 integers b_1, b_2, ..., b_{\frac n 2} (0 β€ b_i β€ 10^{18}) β sequence b, where b_i = a_i + a_{n - i + 1}.
It is guaranteed that there exists at least one correct sequence a, which produces the given sequence b.
Output
Print n integers a_1, a_2, ..., a_n (0 β€ a_i β€ 10^{18}) in a single line.
a_1 β€ a_2 β€ ... β€ a_n should be satisfied.
b_i = a_i + a_{n - i + 1} should be satisfied for all valid i.
Examples
Input
4
5 6
Output
2 3 3 3
Input
6
2 1 2
Output
0 0 1 1 1 2
Submitted Solution:
```
n=int(input())
a=[0 for i in range(0,n)]
b=list(map(int,input().split(" ")))
a[0]=l=0;a[-1]=r=b[0]
for i in range(1,n//2):
if b[i]-l<=r:
a[i]=l;r=a[-(i+1)]=b[i]-l
elif b[i]-r>=l:
a[-(i+1)]=r;l=a[i]=b[i]-r
else: raise RuntimeError("gougoushishabi")
for i in a:
print(i,end=" ")
``` | instruction | 0 | 99,514 | 5 | 199,028 |
Yes | output | 1 | 99,514 | 5 | 199,029 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Mishka is trying really hard to avoid being kicked out of the university. In particular, he was doing absolutely nothing for the whole semester, miraculously passed some exams so that just one is left.
There were n classes of that subject during the semester and on i-th class professor mentioned some non-negative integer a_i to the students. It turned out, the exam was to tell the whole sequence back to the professor.
Sounds easy enough for those who attended every class, doesn't it?
Obviously Mishka didn't attend any classes. However, professor left some clues on the values of a to help out students like Mishka:
* a was sorted in non-decreasing order (a_1 β€ a_2 β€ ... β€ a_n);
* n was even;
* the following sequence b, consisting of \frac n 2 elements, was formed and given out to students: b_i = a_i + a_{n - i + 1}.
Professor also mentioned that any sequence a, which produces sequence b with the presented technique, will be acceptable.
Help Mishka to pass that last exam. Restore any sorted sequence a of non-negative integers, which produces sequence b with the presented technique. It is guaranteed that there exists at least one correct sequence a, which produces the given sequence b.
Input
The first line contains a single integer n (2 β€ n β€ 2 β
10^5) β the length of sequence a. n is always even.
The second line contains \frac n 2 integers b_1, b_2, ..., b_{\frac n 2} (0 β€ b_i β€ 10^{18}) β sequence b, where b_i = a_i + a_{n - i + 1}.
It is guaranteed that there exists at least one correct sequence a, which produces the given sequence b.
Output
Print n integers a_1, a_2, ..., a_n (0 β€ a_i β€ 10^{18}) in a single line.
a_1 β€ a_2 β€ ... β€ a_n should be satisfied.
b_i = a_i + a_{n - i + 1} should be satisfied for all valid i.
Examples
Input
4
5 6
Output
2 3 3 3
Input
6
2 1 2
Output
0 0 1 1 1 2
Submitted Solution:
```
n = int(input())
b = [int(elem) for elem in input().split(" ")]
a = [0]*(n)
a[-1] = b[0]
for i in range(1, len(b)):
if b[i] <= b[i-1]:
if i != 0 and a[i-1] != 0:
a[i] = a[i-1]
a[n-i-1]=b[i]-a[i]
else:
a[i] = 0
a[n-i-1] = b[i]
else:
a[n-i-1] = a[n-i]
a[i] = b[i]-b[i-1]
for i in a:
print(i, end=" ")
print()
``` | instruction | 0 | 99,515 | 5 | 199,030 |
No | output | 1 | 99,515 | 5 | 199,031 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Mishka is trying really hard to avoid being kicked out of the university. In particular, he was doing absolutely nothing for the whole semester, miraculously passed some exams so that just one is left.
There were n classes of that subject during the semester and on i-th class professor mentioned some non-negative integer a_i to the students. It turned out, the exam was to tell the whole sequence back to the professor.
Sounds easy enough for those who attended every class, doesn't it?
Obviously Mishka didn't attend any classes. However, professor left some clues on the values of a to help out students like Mishka:
* a was sorted in non-decreasing order (a_1 β€ a_2 β€ ... β€ a_n);
* n was even;
* the following sequence b, consisting of \frac n 2 elements, was formed and given out to students: b_i = a_i + a_{n - i + 1}.
Professor also mentioned that any sequence a, which produces sequence b with the presented technique, will be acceptable.
Help Mishka to pass that last exam. Restore any sorted sequence a of non-negative integers, which produces sequence b with the presented technique. It is guaranteed that there exists at least one correct sequence a, which produces the given sequence b.
Input
The first line contains a single integer n (2 β€ n β€ 2 β
10^5) β the length of sequence a. n is always even.
The second line contains \frac n 2 integers b_1, b_2, ..., b_{\frac n 2} (0 β€ b_i β€ 10^{18}) β sequence b, where b_i = a_i + a_{n - i + 1}.
It is guaranteed that there exists at least one correct sequence a, which produces the given sequence b.
Output
Print n integers a_1, a_2, ..., a_n (0 β€ a_i β€ 10^{18}) in a single line.
a_1 β€ a_2 β€ ... β€ a_n should be satisfied.
b_i = a_i + a_{n - i + 1} should be satisfied for all valid i.
Examples
Input
4
5 6
Output
2 3 3 3
Input
6
2 1 2
Output
0 0 1 1 1 2
Submitted Solution:
```
import sys
import math
n=int(input())
lisa=[int(x) for x in input().strip().split()]
first,second,prev=[],[],0
for i in range(n//2):
if(i==0):
first.append(0)
second.append(lisa[i])
prev=lisa[i]
else:
if(prev<lisa[i]):
second.append(prev)
first.append(lisa[i]-prev)
else:
second.append(lisa[i])
first.append(0)
prev=lisa[i]
ksd=second[::-1]
mad=first+ksd
print(mad)
``` | instruction | 0 | 99,516 | 5 | 199,032 |
No | output | 1 | 99,516 | 5 | 199,033 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Mishka is trying really hard to avoid being kicked out of the university. In particular, he was doing absolutely nothing for the whole semester, miraculously passed some exams so that just one is left.
There were n classes of that subject during the semester and on i-th class professor mentioned some non-negative integer a_i to the students. It turned out, the exam was to tell the whole sequence back to the professor.
Sounds easy enough for those who attended every class, doesn't it?
Obviously Mishka didn't attend any classes. However, professor left some clues on the values of a to help out students like Mishka:
* a was sorted in non-decreasing order (a_1 β€ a_2 β€ ... β€ a_n);
* n was even;
* the following sequence b, consisting of \frac n 2 elements, was formed and given out to students: b_i = a_i + a_{n - i + 1}.
Professor also mentioned that any sequence a, which produces sequence b with the presented technique, will be acceptable.
Help Mishka to pass that last exam. Restore any sorted sequence a of non-negative integers, which produces sequence b with the presented technique. It is guaranteed that there exists at least one correct sequence a, which produces the given sequence b.
Input
The first line contains a single integer n (2 β€ n β€ 2 β
10^5) β the length of sequence a. n is always even.
The second line contains \frac n 2 integers b_1, b_2, ..., b_{\frac n 2} (0 β€ b_i β€ 10^{18}) β sequence b, where b_i = a_i + a_{n - i + 1}.
It is guaranteed that there exists at least one correct sequence a, which produces the given sequence b.
Output
Print n integers a_1, a_2, ..., a_n (0 β€ a_i β€ 10^{18}) in a single line.
a_1 β€ a_2 β€ ... β€ a_n should be satisfied.
b_i = a_i + a_{n - i + 1} should be satisfied for all valid i.
Examples
Input
4
5 6
Output
2 3 3 3
Input
6
2 1 2
Output
0 0 1 1 1 2
Submitted Solution:
```
n=int(input())
b=[int(i) for i in input().split()]
a=[0]*n
a[0]=0
a[n-1]=b[0]
for i in range(1,n//2):
if b[i]<=b[i-1]:
a[i]=a[i-1]
else:
a[i]=a[i-1]+1
a[n-i-1]=b[i]-a[i]
print(a)
``` | instruction | 0 | 99,517 | 5 | 199,034 |
No | output | 1 | 99,517 | 5 | 199,035 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Mishka is trying really hard to avoid being kicked out of the university. In particular, he was doing absolutely nothing for the whole semester, miraculously passed some exams so that just one is left.
There were n classes of that subject during the semester and on i-th class professor mentioned some non-negative integer a_i to the students. It turned out, the exam was to tell the whole sequence back to the professor.
Sounds easy enough for those who attended every class, doesn't it?
Obviously Mishka didn't attend any classes. However, professor left some clues on the values of a to help out students like Mishka:
* a was sorted in non-decreasing order (a_1 β€ a_2 β€ ... β€ a_n);
* n was even;
* the following sequence b, consisting of \frac n 2 elements, was formed and given out to students: b_i = a_i + a_{n - i + 1}.
Professor also mentioned that any sequence a, which produces sequence b with the presented technique, will be acceptable.
Help Mishka to pass that last exam. Restore any sorted sequence a of non-negative integers, which produces sequence b with the presented technique. It is guaranteed that there exists at least one correct sequence a, which produces the given sequence b.
Input
The first line contains a single integer n (2 β€ n β€ 2 β
10^5) β the length of sequence a. n is always even.
The second line contains \frac n 2 integers b_1, b_2, ..., b_{\frac n 2} (0 β€ b_i β€ 10^{18}) β sequence b, where b_i = a_i + a_{n - i + 1}.
It is guaranteed that there exists at least one correct sequence a, which produces the given sequence b.
Output
Print n integers a_1, a_2, ..., a_n (0 β€ a_i β€ 10^{18}) in a single line.
a_1 β€ a_2 β€ ... β€ a_n should be satisfied.
b_i = a_i + a_{n - i + 1} should be satisfied for all valid i.
Examples
Input
4
5 6
Output
2 3 3 3
Input
6
2 1 2
Output
0 0 1 1 1 2
Submitted Solution:
```
# your code goes here
from collections import defaultdict
import bisect
from itertools import accumulate
import os
import sys
import math
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)
def input(): return sys.stdin.readline().rstrip("\r\n")
# ------------------- fast io --------------------
n=int(input())
b=list(map(int,input().split()))
ans=[0]*(n)
l=0
r=10*18
for i in range(n//2):
ans[i]=max(l,b[i]-r)
ans[-i-1]=b[i]-ans[i]
l=ans[i]
r=b[i]-ans[i]
print(*ans)
``` | instruction | 0 | 99,518 | 5 | 199,036 |
No | output | 1 | 99,518 | 5 | 199,037 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let f_{x} = c^{2x-6} β
f_{x-1} β
f_{x-2} β
f_{x-3} for x β₯ 4.
You have given integers n, f_{1}, f_{2}, f_{3}, and c. Find f_{n} mod (10^{9}+7).
Input
The only line contains five integers n, f_{1}, f_{2}, f_{3}, and c (4 β€ n β€ 10^{18}, 1 β€ f_{1}, f_{2}, f_{3}, c β€ 10^{9}).
Output
Print f_{n} mod (10^{9} + 7).
Examples
Input
5 1 2 5 3
Output
72900
Input
17 97 41 37 11
Output
317451037
Note
In the first example, f_{4} = 90, f_{5} = 72900.
In the second example, f_{17} β 2.28 Γ 10^{29587}.
Submitted Solution:
```
#!/usr/bin/env python
class Mat:
def __init__(self, x):
if x == 1: # identity
self.m = [
[1, 0, 0],
[0, 1, 0],
[0, 0, 1],
]
else: # x should be 3x3
self.m = [[
x[i][j]
for j in range(3)] for i in range(3)]
def __mul__(self, other):
return Mat([[
(sum(self.m[i][k] * other.m[k][j] for k in range(3))) % (mod - 1)
for j in range(3)] for i in range(3)])
def __rmul__(self, other):
return Mat([[
(sum(other.m[i][k] * self.m[k][j] for k in range(3))) % (mod - 1)
for j in range(3)] for i in range(3)])
def __mod__(self, _mod):
return Mat([[
self.m[i][j] % _mod
for j in range(3)] for i in range(3)])
def mat_bin_mod_pow(_mat, _mod, _pow):
if _pow == 0:
return Mat(1)
return (mat_bin_mod_pow((_mat * _mat) % _mod, _mod, _pow >> 1) *
(_mat if _pow & 1 else Mat(1))) % _mod
def bin_mod_pow(_num, _mod, _pow):
if _pow == 0:
return 1
return (bin_mod_pow(_num**2 % _mod, _mod, _pow >> 1) *
(_num if _pow & 1 else 1)) % _mod
def bin_mod_inv(_num, _mod):
return bin_mod_pow(_num, _mod, _mod - 2) % _mod
if __name__ == "__main__":
mod = 10**9 + 7
n, f1, f2, f3, c = map(int, input().split())
f = [f1, f2, f3]
g = [(f[i] * c**(i + 1)) % mod for i in range(3)]
mat = Mat([
[0, 1, 0],
[0, 0, 1],
[1, 1, 1],
])
p = mat_bin_mod_pow(_mat=mat, _mod=mod-1, _pow=n-3).m[-1]
print((
bin_mod_pow(_num=g[0], _mod=mod, _pow=p[0]) *
bin_mod_pow(_num=g[1], _mod=mod, _pow=p[1]) *
bin_mod_pow(_num=g[2], _mod=mod, _pow=p[2]) *
bin_mod_pow(_num=bin_mod_inv(_num=c, _mod=mod), _mod=mod, _pow=n)
) % mod)
``` | instruction | 0 | 99,559 | 5 | 199,118 |
Yes | output | 1 | 99,559 | 5 | 199,119 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let f_{x} = c^{2x-6} β
f_{x-1} β
f_{x-2} β
f_{x-3} for x β₯ 4.
You have given integers n, f_{1}, f_{2}, f_{3}, and c. Find f_{n} mod (10^{9}+7).
Input
The only line contains five integers n, f_{1}, f_{2}, f_{3}, and c (4 β€ n β€ 10^{18}, 1 β€ f_{1}, f_{2}, f_{3}, c β€ 10^{9}).
Output
Print f_{n} mod (10^{9} + 7).
Examples
Input
5 1 2 5 3
Output
72900
Input
17 97 41 37 11
Output
317451037
Note
In the first example, f_{4} = 90, f_{5} = 72900.
In the second example, f_{17} β 2.28 Γ 10^{29587}.
Submitted Solution:
```
def _mul(A, B, MOD):
C = [[0] * len(B[0]) for i in range(len(A))]
for i in range(len(A)):
for k in range(len(B)):
for j in range(len(B[0])):
C[i][j] = (C[i][j] + A[i][k]*B[k][j]) % MOD
return C
def pow_matrix(A, n, MOD):
"""A**nγγγγͺγ³γ°γ«γγ£γ¦ζ±γγ"""
B = [[0] * len(A) for i in range(len(A))]
for i in range(len(A)):
B[i][i] = 1
while n > 0:
if n & 1:
B = _mul(A, B, MOD)
A = _mul(A, A, MOD)
n = n // 2
return B
n, f1, f2, f3, c = map(int, input().split())
MOD = 10**9 + 7
ans = 1
matrix = [[0]*3 for i in range(3)]
matrix[0][0] = matrix[0][1] = matrix[0][2] =1
matrix[1][0] = 1
matrix[2][1] = 1
f_matrix = pow_matrix(matrix, n - 3, MOD - 1)
ans *= pow(f3, f_matrix[0][0], MOD)
ans *= pow(f2, f_matrix[0][1], MOD)
ans *= pow(f1, f_matrix[0][2], MOD)
matrix = [[0]*5 for i in range(5)]
matrix[0][0] = matrix[0][1] = matrix[0][2] =1
matrix[0][3] = 2
matrix[0][4] = -6
matrix[1][0] = matrix[2][1] = 1
matrix[3][3] = matrix[3][4] = 1
matrix[4][4] = 1
c_matrix = pow_matrix(matrix, n - 3, MOD - 1)
ans *= pow(c, c_matrix[0][3] * 4 + c_matrix[0][4], MOD)
print(ans % MOD)
``` | instruction | 0 | 99,560 | 5 | 199,120 |
Yes | output | 1 | 99,560 | 5 | 199,121 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let f_{x} = c^{2x-6} β
f_{x-1} β
f_{x-2} β
f_{x-3} for x β₯ 4.
You have given integers n, f_{1}, f_{2}, f_{3}, and c. Find f_{n} mod (10^{9}+7).
Input
The only line contains five integers n, f_{1}, f_{2}, f_{3}, and c (4 β€ n β€ 10^{18}, 1 β€ f_{1}, f_{2}, f_{3}, c β€ 10^{9}).
Output
Print f_{n} mod (10^{9} + 7).
Examples
Input
5 1 2 5 3
Output
72900
Input
17 97 41 37 11
Output
317451037
Note
In the first example, f_{4} = 90, f_{5} = 72900.
In the second example, f_{17} β 2.28 Γ 10^{29587}.
Submitted Solution:
```
MD = 10**9+7
def mult(A,B):
n = len(A)
C = [[0] * n for _ in range(n)]
for i in range(len(A)):
for j in range(len(A)):
for k in range(len(A)):
C[i][j] += A[i][k]*B[k][j]
C[i][j] %= MD-1
return C
def ex(A,k):
n = len(A)
R = [[0] * n for _ in range(n)]
for i in range(n):
R[i][i] = 1
while k > 0:
if k & 1:
R = mult(R,A)
k //= 2
A = mult(A,A)
return R
cma = [
[1,1,1,1,0],
[1,0,0,0,0],
[0,1,0,0,0],
[0,0,0,1,2],
[0,0,0,0,1]
]
tri = [
[1,1,1],
[1,0,0],
[0,1,0]
]
n,f1,f2,f3,c = map(int,input().split())
ce = ex(cma,n-3)
cp = ce[0][3]*2+ce[0][4]
f = ex(tri,n-3)
fp1 = f[0][2]
fp2 = f[0][1]
fp3 = f[0][0]
r = pow(f1,fp1,MD)*pow(f2,fp2,MD)*pow(f3,fp3,MD)*pow(c,cp,MD)
#print(fp1,fp2,fp3,cp)
print(r%MD)
``` | instruction | 0 | 99,561 | 5 | 199,122 |
Yes | output | 1 | 99,561 | 5 | 199,123 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let f_{x} = c^{2x-6} β
f_{x-1} β
f_{x-2} β
f_{x-3} for x β₯ 4.
You have given integers n, f_{1}, f_{2}, f_{3}, and c. Find f_{n} mod (10^{9}+7).
Input
The only line contains five integers n, f_{1}, f_{2}, f_{3}, and c (4 β€ n β€ 10^{18}, 1 β€ f_{1}, f_{2}, f_{3}, c β€ 10^{9}).
Output
Print f_{n} mod (10^{9} + 7).
Examples
Input
5 1 2 5 3
Output
72900
Input
17 97 41 37 11
Output
317451037
Note
In the first example, f_{4} = 90, f_{5} = 72900.
In the second example, f_{17} β 2.28 Γ 10^{29587}.
Submitted Solution:
```
# @author
import sys
class EProductOrientedRecurrence:
def solve(self):
MOD = 10 ** 9 + 7
D = 3
I = [
[1 if i == j else 0 for j in range(D)]
for i in range(D)
]
def mat_mult(A, B):
n, m, p = len(A), len(A[0]), len(B[0])
assert (len(B) == m)
C = [[0] * p for _ in range(n)]
for i in range(n):
for k in range(m):
Aik = A[i][k]
for j in range(p):
C[i][j] = (C[i][j] + Aik * B[k][j]) % (MOD - 1)
return C
def mat_pow(A, p):
if p == 0:
return I
if p == 1:
return A
if p % 2 == 0:
return mat_pow(mat_mult(A, A), p // 2)
else:
return mat_mult(A, mat_pow(A, p - 1))
n, f1, f2, f3, c = [int(_) for _ in input().split()]
M = [[0, 1, 0],
[0, 0, 1],
[1, 1, 1]]
Rf1 = mat_mult(mat_pow(M, n - 1), [[1], [0], [0]])[0][0]
Rf2 = mat_mult(mat_pow(M, n - 1), [[0], [1], [0]])[0][0]
Rf3 = mat_mult(mat_pow(M, n - 1), [[0], [0], [1]])[0][0]
Rpower = (mat_mult(mat_pow(M, n - 1), [[1], [2], [3]])[0][0] - n) % (MOD - 1)
ans = pow(f1, Rf1, MOD) * pow(f2, Rf2, MOD) * pow(f3, Rf3, MOD) * pow(c, Rpower, MOD)
ans %= MOD
print(ans)
solver = EProductOrientedRecurrence()
input = sys.stdin.readline
solver.solve()
``` | instruction | 0 | 99,562 | 5 | 199,124 |
Yes | output | 1 | 99,562 | 5 | 199,125 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let f_{x} = c^{2x-6} β
f_{x-1} β
f_{x-2} β
f_{x-3} for x β₯ 4.
You have given integers n, f_{1}, f_{2}, f_{3}, and c. Find f_{n} mod (10^{9}+7).
Input
The only line contains five integers n, f_{1}, f_{2}, f_{3}, and c (4 β€ n β€ 10^{18}, 1 β€ f_{1}, f_{2}, f_{3}, c β€ 10^{9}).
Output
Print f_{n} mod (10^{9} + 7).
Examples
Input
5 1 2 5 3
Output
72900
Input
17 97 41 37 11
Output
317451037
Note
In the first example, f_{4} = 90, f_{5} = 72900.
In the second example, f_{17} β 2.28 Γ 10^{29587}.
Submitted Solution:
```
import math
md = 10**9+7
def multiply(M,N):
md = 10**9+7
R = [[0 for i in range(3)] for j in range(3)]
for i in range(0, 3):
for j in range(0, 3):
for k in range(0, 3):
R[i][j] += (M[i][k] * N[k][j])%md
R[i][j] %= md
return R
def power(mat, n):
res = [[1,0,0],[0,1,0],[0,0,1]]
while n:
if n&1: res = multiply(res, mat)
mat = multiply(mat, mat)
n//=2
return res
n, f1, f2, f3, c = map(int, input().split())
f1 = (f1*c)%md
f2 = (f2*c**2)%md
f3 = (f3*c**3)%md
mat = [[1,1,1],[1,0,0],[0,1,0]]
res = power(mat, n-3)
pw1, pw2, pw3 = res[0][2], res[0][1], res[0][0]
f1 = pow(f1, pw1, md)
f2 = pow(f2, pw2, md)
f3 = pow(f3, pw3, md)
ans = ((f1 * f2)%md * f3)%md
c = pow(c, md-2, md)
ans *= pow(c, n, md)
ans %= md
print(ans)
``` | instruction | 0 | 99,563 | 5 | 199,126 |
No | output | 1 | 99,563 | 5 | 199,127 |
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