Problems
The Function
The Function
Given an positive integer N, compute the following function f(N):
Here x/i denotes integer division.
Since the F(N) can be quite large; please output F(N) % 1000000007.
Input data
First line contains T, the number of test cases. Next T lines contain the value of N for each test case.
It is known that 1 ≤ T ≤ 50, 1 ≤ N ≤ 10^9.
Output data
Output T lines, i-th line containing the answer for i-th test case.
Examples
Input example #1
50 16808 282475250 622650074 984943659 144108931 470211273 101027545 457850879 458777924 7237710 823564441 115438166 784484493 74243043 114807988 137522504 441282328 16531730 823378841 143542613 896544304 474833170 264817710 998097158 817129561 131570934 197493100 404280279 893351817 505795336 954899098 636807827 563613513 101929268 580723811 704877634 358580980 624379150 128236580 784558822 530511968 110010673 551901394 617819337 399125486 156091746 356425229 899894092 585640195 937186358
Output example #1
798891814 965597375 781629348 231400999 681820990 326512869 570253390 553618273 729705082 172153172 840905619 926147771 473302851 222933489 780491825 292562451 160305720 354723852 873364684 711644071 900530547 427807301 376833173 86908677 258244673 663554101 778321897 623547825 471574703 743517145 408116618 272491640 207875466 268455915 739468574 509513128 508783180 566031677 168576807 488778900 265663314 77697112 413399613 670920154 128767216 688934127 376560969 975499331 669113588 391639208