Time Limit: 2 Seconds      Memory Limit: 65536 KB

##Description
Recently, LBH is learning the curse linear algebra. Thus he is very interested in matrix and determinant now. In order to practice his ability of solving the problem of linear algebra, he just invent some problems by himself. Once the problems was create, he would solve it immediately. However, he meet a problem that was so hard that he couldn’t work out even though racked his brains. The problem was described as follow:

To a integer martix Mnn(aij), we define two function add(Mnn(aij))=Mnn(aij + 1) and sub(Mnn(aij))=Mnn(aij - 1) which were exactly like this:

a串： 110110110，则：

b`串：1011<——这里才是原来b串的头。但是向上对应到a串时，已经是m-1这个位置了。所以说，小于m-1的卷积是没有意义的。

##description
Emperor Palpatine has been ruling the Empire for 25 years and Darth Vader has been the head of the Empire Armed Forces. However, the Rebel movement is strong like it never used to be. One of the rebel leaders, Princess Leia from Alderaan, managed to get hold of secret blueprints of the Death Star, the imperial war station.

The Princess was going to deliver the station plan to the secret base for further analysis and searching for vulnerable spots. But her ship was attacked by the space destroyer “Devastator” headed by Darth Vader. At the last moment Princess Leia managed to send her findings to one of the closest planet called Tatooine with her droid R2-D2. Quite conveniently, an old friend of her father Obi-Wan Kenobi lives on that planet.

Time Limit: 20001000 MS (Java/Others)    Memory Limit: 6553665536 K (Java/Others)
Total Submission(s): 612    Accepted Submission(s): 310

Problem Description
Teacher Mai has an integer x. He does the following operations k times. In the i-th operation, x becomes the least integer no less than x, which is the multiple of i. He wants to know what is the number x now.

Time Limit: 90004500 MS (Java/Others)    Memory Limit: 131072131072 K (Java/Others)
Total Submission(s): 166    Accepted Submission(s): 76

Problem Description
FSF has programmed a game. In this game, players need to divide a rectangle into several same squares. The length and width of rectangles are integer, and of course the side length of squares are integer. After division, players can get some coins. If players successfully divide a AxB rectangle(length: A, width: B) into KxK squares(side length: K), they can get A*B/ gcd(A/K,B/K) gold coins. In a level, you can’t get coins twice with same method. (For example, You can get 6 coins from 2x2(A=2,B=2) rectangle. When K=1, A*B/gcd(A/K,B/K)=2; When K=2, A*B/gcd(A/K,B/K)=4; 2+4=6; ) There are N*(N+1)/2 levels in this game, and every level is an unique rectangle. (1x1 , 2x1, 2x2, 3x1, ..., Nx(N-1), NxN) FSF has played this game for a long time, and he finally gets all the coins in the game. Unfortunately ,he uses an UNSIGNED 32-BIT INTEGER variable to count the number of coins. This variable may overflow. We want to know what the variable will be. (In other words, the number of coins mod 2^32)