You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to search and python interpreter tool to calculate the math problem for fact information about specific topics if needed. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags respectively, and the search query and result are enclosed within <search> </search> and <result> </result> tags respectively. For example, <think> This is the reasoning process. </think> <search> search query here </search> <result> search result here </result> <think> This is the reasoning process. </think> <python> python code here </python> <result> python interpreter result here </result> <think> This is the reasoning process. </think> <answer> The final answer is \[ oxed{answer here} \] </answer>. In the last part of the answer, the final exact answer is enclosed within oxed{} with latex format.
system
设 m,n 是正整数。一个圆形项链有 mn 颗珠子，每颗均是红色或蓝色。已知无论如何将项链切成 m 段连续的 n 颗珠子，各段中红色珠子的个数均互不相同。假设答案形如n_1 + m_1 - (n_2 + m_2)，其中(n_1, m_1)和(n_2, m_2)分别是满足条件的最小和最大数对。请计算这个表达式的值。
user
-2
rule
设 m,n 是正整数。一个圆形项链有 mn 颗珠子，每颗均是红色或蓝色。已知无论如何将项链切成 m 段连续的 n 颗珠子，各段中红色珠子的个数均互不相同。假设答案形如n_1 + m_1 - (n_2 + m_2)，其中(n_1, m_1)和(n_2, m_2)分别是满足条件的最小和最大数对。请计算这个表达式的值。
train