HBC237448[HEOI2012]采花,数据结构,线段树,树状数组gcds题解

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For any positive integer sequence a1,a2,,ama_1,a_2,cdots,a_ma1,a2,,am, define its weight f=∑i>1gcdwf=sum_{i>1} gcdcdot wf=∑i>1gcdw， Here w=px3+qx2+rxw=px^3+qx^2+rxw=px3+qx2+rx. p,q,r,mp,q,r,mp,q,r,m are given constants， Calculate the sum of the weight of all such sequences whose sum is nnn， The answer might be very huge, print it module 109+710^9+7109+7.

For any positive integer sequence a1,a2,⋯ ,ama_1,a_2,cdots,a_ma1​,a2​,⋯,am​, define its weight f(a)=∑i>1gcd⁡(ai,ai−1)⋅w(ai)f(a)=sum_{i>1} gcd(a_i,a_{i-1})cdot w(a_i)f(a)=∑i>1​gcd(ai​,ai−1​)⋅w(ai​)。 Here w(x)=px3+qx2+rxw(x)=px^3+qx^2+rxw(x)=px3+qx2+rx. p,q,r,mp,q,r,mp,q,r,m are given constants。 Calculate the sum of the weight of all such sequences whose sum is nnn。 The answer might be very huge, print it module 109+710^9+7109+7.

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标签： HBC237448[HEOI2012]采花 数据结构 线段树 树状数组gcds题解