ans=∑c∏i=1n(ai+ci−1−ci)→∑c∑S⊆{0,1,2,⋯ ,n}∏i∈S(ai−ci)∏i∉Sci−1ans=\sum\limits_{c}\prod\limits_{i=1}^{n}(a_i+c_{i-1}-c_i)\to \sum\limits_{c}\sum\limits_{S\subseteq \{0,1,2,\cdots,n\}}\prod\limits_{i\in S} (a_i-c_{i})\prod\limits_{i\not\in S}c_{i-1}ans=c∑i=1∏n(ai+ci−1−ci)→c∑S⊆{0,1,2,⋯,n}∑i∈S∏(ai−ci)i∈S∏ci−1
