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237 lines
5.3 KiB
Python
Executable file
237 lines
5.3 KiB
Python
Executable file
"""#
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### 谜题描述
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Simon has a prime number x and an array of non-negative integers a1, a2, ..., an.
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Simon loves fractions very much. Today he wrote out number <image> on a piece of paper. After Simon led all fractions to a common denominator and summed them up, he got a fraction: <image>, where number t equals xa1 + a2 + ... + an. Now Simon wants to reduce the resulting fraction.
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Help him, find the greatest common divisor of numbers s and t. As GCD can be rather large, print it as a remainder after dividing it by number 1000000007 (109 + 7).
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Input
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The first line contains two positive integers n and x (1 ≤ n ≤ 105, 2 ≤ x ≤ 109) — the size of the array and the prime number.
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The second line contains n space-separated integers a1, a2, ..., an (0 ≤ a1 ≤ a2 ≤ ... ≤ an ≤ 109).
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Output
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Print a single number — the answer to the problem modulo 1000000007 (109 + 7).
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Examples
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Input
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2 2
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2 2
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Output
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8
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Input
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3 3
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1 2 3
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Output
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27
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Input
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2 2
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29 29
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Output
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73741817
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Input
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4 5
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0 0 0 0
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Output
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1
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Note
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In the first sample <image>. Thus, the answer to the problem is 8.
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In the second sample, <image>. The answer to the problem is 27, as 351 = 13·27, 729 = 27·27.
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In the third sample the answer to the problem is 1073741824 mod 1000000007 = 73741817.
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In the fourth sample <image>. Thus, the answer to the problem is 1.
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Here is a reference code to solve this task. You can use this to help you genereate cases or validate the solution.
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```python
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# coding: utf-8
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# Laybson Plismenn / UFCG - 2015
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mod = 1000000007
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def min(a,b):
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if a<b :
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return a
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else:
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return b
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def Pow(a,b):
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d=1
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t=a
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while b>0:
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if b%2==1:
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d=d*t%mod
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b/=2
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t=t*t%mod
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return d
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a=[]
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b=[]
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vis=[]
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sum=0
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n,x=map(int,raw_input().split())
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a=(map(int,raw_input().split()))
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for i in range(len(a)):
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sum += a[i]
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for i in range(len(a)):
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b.append(sum-a[i])
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vis.append(0)
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Max=sum+10
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ans=1
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while True:
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Ma = Max
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for i in range(len(b)):
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if vis[i]==0 :
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Ma=min(Ma,b[i])
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if (Ma==0 or Ma==Max):
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break
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ans *= Pow(x,Ma)
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ans %= mod
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num=0
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for i in range(len(b)):
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b[i] -= Ma
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if(b[i]==0):
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num+=1
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sum = sum-Ma
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if (sum<=0 or num%x != 0):
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break
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else :
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p=0
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for i in range(len(b)):
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if(b[i]==0):
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if(p < num/x):
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b[i]=1
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p+=1
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else :
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vis[i]=1
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print ans
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```
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请完成上述谜题的训练场环境类实现，包括所有必要的方法。
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"""
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from bootcamp import Basebootcamp
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import random
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from bootcamp import Basebootcamp
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mod = 10**9 + 7
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def calculate_gcd_mod(n, x, a_list):
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sum_total = sum(a_list)
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b = [sum_total - ai for ai in a_list]
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vis = [False] * n
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ans = 1
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while True:
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current_min = None
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for i in range(n):
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if not vis[i] and (current_min is None or b[i] < current_min):
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current_min = b[i]
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if current_min is None or current_min == 0:
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break
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ans = ans * pow(x, current_min, mod) % mod
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count = 0
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new_sum = sum_total - current_min
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for i in range(n):
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if not vis[i]:
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b[i] -= current_min
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if b[i] == 0:
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count += 1
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sum_total = new_sum
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if sum_total <= 0 or count % x != 0:
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break
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else:
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target = count // x
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p = 0
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for i in range(n):
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if not vis[i] and b[i] == 0:
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if p < target:
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b[i] = 1
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p += 1
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else:
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vis[i] = True
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return ans % mod
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class Cprimenumberbootcamp(Basebootcamp):
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def __init__(self, max_n=5, x_primes=None, a_max=10):
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super().__init__()
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self.max_n = max_n
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self.x_primes = x_primes if x_primes is not None else [2, 3, 5, 7, 11]
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self.a_max = a_max
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def case_generator(self):
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n = random.randint(1, self.max_n)
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x = random.choice(self.x_primes)
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a = sorted(random.randint(0, self.a_max) for _ in range(n))
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correct_answer = calculate_gcd_mod(n, x, a)
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return {
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'n': n,
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'x': x,
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'a': a,
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'correct_answer': correct_answer
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}
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@staticmethod
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def prompt_func(question_case):
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n = question_case['n']
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x = question_case['x']
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a = question_case['a']
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a_str = ' '.join(map(str, a))
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return f"""Simon has a prime number x and an array of non-negative integers. Your task is to compute the GCD of the fraction's numerator and denominator after summing 1/x^a_i for all elements.
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Input:
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First line: {n} {x} (n and the prime x)
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Second line: {a_str} (non-decreasing array)
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Calculate the GCD modulo 1,000,000,007. Put your final answer within [answer] and [/answer] tags. Example: [answer]42[/answer]."""
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@staticmethod
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def extract_output(output):
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import re
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matches = re.findall(r'\[answer\](.*?)\[/answer\]', output, re.DOTALL)
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if not matches:
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return None
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last_answer = matches[-1].strip()
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try:
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number_str = ''.join(c for c in last_answer if c.isdigit())
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return int(number_str) if number_str else None
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except:
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return None
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@classmethod
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def _verify_correction(cls, solution, identity):
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if solution is None:
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return False
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return solution == identity['correct_answer']
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