去年的 tangjz 非常喜欢做数论题，但是一年以后的 tangjz 却不那么会做了。

在整理以前的试题时，他发现了这样一道题目：“求 ∑σ(i) ，其中 1≤i≤N ， σ(i) 表示 i 的约数之和。”

现在他长大了，题目也变难了，所以麻烦你来帮他解决一道数论题吧。

他需要你求如下表达式的值：

∑Ni=1∑Nj=1max(i,j)⋅ σ(i⋅ j)

其中 max(i,j) 表示 i 和 j 里的最大值， σ(i⋅ j) 表示 i⋅ j 的约数之和。

例如当 N=2 的时候，由 σ(1)=1,σ(2)=1+2=3,σ(4)=1+2+4=7 可知，答案应为 1⋅ σ(1⋅ 1)+2⋅ σ(1⋅ 2)+2⋅ σ(2⋅ 1)+2⋅ σ(2⋅ 2)=27 。

他发现答案有点大，所以你只需要告诉他答案模 1000000007 的值即可。-Last year s tangjz love do theory very much, but a year later, tangjz is not so do.

In order to previous questions, he found such a topic:　sigma sigma (I), and 1 = I = N, sigma (I) representation and approximate i.

Now that he s grown up, the problem is hard, so you can help him solve a problem.

He needs you to ask the value of the expression as follows:

Sigma Sigma Ni=1 Nj=1max (I, J) Sigma (I J)

The max (I, J) said the maximum values of I and j, sigma (I J) and I said about J.

For example, when N=2, by =1 (1), sigma sigma sigma (2) =1+2=3 (4) =1+2+4=7 shows that the answer should be 1 sigma (1 1)+2 (1 sigma 2 sigma (2)+2 1 sigma (2)+2 2) =27.

He found that the answer is a little big, so you just need to tell him the answer to 1000000007 of the value can be.