 Birthday Cake

Description
Prince Remmarguts helped Uyuw successfully hold a concert in our previous story (POJ 2451), and ...that was the day of Uyuw's birthday.
Tingaling, the chef was called on by Remmarguts. "You must prepare an immense birthday cake for lovely Princess Uyuw in a single day," said Remmarguts. Though Remmarguts' order is outrageous, the chef eventually rushed to buy flour, sugar, fat, and some other ingredients.
There had been chaos caused by war for quite a long time. The price of everything has been highly raised. Being the head accountant of country UDF – United Delta of Freedom, you must weight the cake carefully to make sure the chef did not perform a cheat on the ingredients.
The cake is made up of N levels. There is a 'cube' in each level, while the length of cube on kth level (count from the topmost) is exactly k! For Remmarguts lives in an MDimension world unlike our, you should notice that the 'cube' here means MDimension cube, and the volume of a cube with length k is k ^ M.
You are to calculate the total volume of such an immense cake.
InputYou should read the number of test cases Z (Z <= 30) in the first line. Each of the following lines denotes a single test case, consisting of two integers N and M. We guarantee that 1 <= N <= 10 ^ 41 and 3 <= M <= 100.
OutputOutput one line per test case, showing the total volume of that cake. We also guarantee that the volume is less than 10 ^ 250.
Sample Input2
3 3
6 5
Sample Output36
12201
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 Problem Description Today is the birthday of Mr. Bon Vivant, who is known as one of the greatest p鈚issiers in the world. Those who are invited to his birthday party are gourmets from around the world. They are eager to see and eat his extremely creative cakes. Now a large boxshaped cake is being carried into the party. It is not beautifully decorated and looks rather simple, but it must be delicious beyond anyone's imagination. Let us cut it into pieces with a knife and serve them to the guests attending the party. The cake looks rectangular, viewing from above (Figure C1). As exemplified in Figure C2, the cake will iteratively be cut into pieces, where on each cut exactly a single piece is cut into two smaller pieces. Each cut surface must be orthogonal to the bottom face and must be orthogonal or parallel to a side face. So, every piece shall be rectangular looking from above and every side face vertical. Figure C1: The top view of the cake Figure C2: Cutting the cake into pieces Piece sizes in Figure C2 vary significantly and it may look unfair, but you don't have to worry. Those guests who would like to eat as many sorts of cakes as possible often prefer smaller pieces. Of course, some prefer larger ones. Your mission of this problem is to write a computer program that simulates the cutting process of the cake and reports the size of each piece. Input The input is a sequence of datasets, each of which is of the following format. n w d p1 s1 ... pn sn The first line starts with an integer n that is between 0 and 100 inclusive. It is the number of cuts to be performed. The following w and d in the same line are integers between 1 and 100 inclusive. They denote the width and depth of the cake, respectively. Assume in the sequel that the cake is placed so that w and d are the lengths in the eastwest and northsouth directions, respectively. Each of the following n lines specifies a single cut, cutting one and only one piece into two. pi is an integer between 1 and i inclusive and is the identification number of the piece that is the target of the ith cut. Note that, just before the ith cut, there exist exactly i pieces. Each piece in this stage has a unique identification number that is one of 1, 2, ..., i and is defined as follows: * The earlier a piece was born, the smaller its identification number is. * Of the two pieces born at a time by the same cut, the piece with the smaller area (looking from above) has the smaller identification number. If their areas are the same, you may define as you like the order between them, since your choice in this case has no influence on the final answer. Note that identification numbers are adjusted after each cut. si is an integer between 1 and 1000 inclusive and specifies the starting point of the ith cut. From the northwest corner of the piece whose identification number is pi, you can reach the starting point by traveling si in the clockwise direction around the piece. You may assume that the starting point determined in this way cannot be any one of the four corners of the piece. The ith cut surface is orthogonal to the side face on which the starting point exists. The end of the input is indicated by a line with three zeros. Output For each dataset, print in a line the areas looking from above of all the pieces that exist upon completion of the n cuts specified in the dataset. They should be in ascending order and separated by a space. When multiple pieces have the same area, print it as many times as the number of the pieces. Sample Input 3 5 6 1 18 2 19 1 2 3 4 1 1 1 2 1 3 1 0 2 5 0 0 0 Sample Output 4 4 6 16 1 1 1 1 10
 分蛋糕的问题，Cut the Cake
 Problem Description Today is the birthday of Mr. Bon Vivant, who is known as one of the greatest p鈚issiers in the world. Those who are invited to his birthday party are gourmets from around the world. They are eager to see and eat his extremely creative cakes. Now a large boxshaped cake is being carried into the party. It is not beautifully decorated and looks rather simple, but it must be delicious beyond anyone's imagination. Let us cut it into pieces with a knife and serve them to the guests attending the party. The cake looks rectangular, viewing from above (Figure C1). As exemplified in Figure C2, the cake will iteratively be cut into pieces, where on each cut exactly a single piece is cut into two smaller pieces. Each cut surface must be orthogonal to the bottom face and must be orthogonal or parallel to a side face. So, every piece shall be rectangular looking from above and every side face vertical. Figure C1: The top view of the cake Figure C2: Cutting the cake into pieces Piece sizes in Figure C2 vary significantly and it may look unfair, but you don't have to worry. Those guests who would like to eat as many sorts of cakes as possible often prefer smaller pieces. Of course, some prefer larger ones. Your mission of this problem is to write a computer program that simulates the cutting process of the cake and reports the size of each piece. Input The input is a sequence of datasets, each of which is of the following format. n w d p1 s1 ... pn sn The first line starts with an integer n that is between 0 and 100 inclusive. It is the number of cuts to be performed. The following w and d in the same line are integers between 1 and 100 inclusive. They denote the width and depth of the cake, respectively. Assume in the sequel that the cake is placed so that w and d are the lengths in the eastwest and northsouth directions, respectively. Each of the following n lines specifies a single cut, cutting one and only one piece into two. pi is an integer between 1 and i inclusive and is the identification number of the piece that is the target of the ith cut. Note that, just before the ith cut, there exist exactly i pieces. Each piece in this stage has a unique identification number that is one of 1, 2, ..., i and is defined as follows: * The earlier a piece was born, the smaller its identification number is. * Of the two pieces born at a time by the same cut, the piece with the smaller area (looking from above) has the smaller identification number. If their areas are the same, you may define as you like the order between them, since your choice in this case has no influence on the final answer. Note that identification numbers are adjusted after each cut. si is an integer between 1 and 1000 inclusive and specifies the starting point of the ith cut. From the northwest corner of the piece whose identification number is pi, you can reach the starting point by traveling si in the clockwise direction around the piece. You may assume that the starting point determined in this way cannot be any one of the four corners of the piece. The ith cut surface is orthogonal to the side face on which the starting point exists. The end of the input is indicated by a line with three zeros. Output For each dataset, print in a line the areas looking from above of all the pieces that exist upon completion of the n cuts specified in the dataset. They should be in ascending order and separated by a space. When multiple pieces have the same area, print it as many times as the number of the pieces. Sample Input 3 5 6 1 18 2 19 1 2 3 4 1 1 1 2 1 3 1 0 2 5 0 0 0 Sample Output 4 4 6 16 1 1 1 1 10
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 Cut the Cake
 Problem Description Today is the birthday of Mr. Bon Vivant, who is known as one of the greatest p鈚issiers in the world. Those who are invited to his birthday party are gourmets from around the world. They are eager to see and eat his extremely creative cakes. Now a large boxshaped cake is being carried into the party. It is not beautifully decorated and looks rather simple, but it must be delicious beyond anyone's imagination. Let us cut it into pieces with a knife and serve them to the guests attending the party. The cake looks rectangular, viewing from above (Figure C1). As exemplified in Figure C2, the cake will iteratively be cut into pieces, where on each cut exactly a single piece is cut into two smaller pieces. Each cut surface must be orthogonal to the bottom face and must be orthogonal or parallel to a side face. So, every piece shall be rectangular looking from above and every side face vertical. Figure C1: The top view of the cake Figure C2: Cutting the cake into pieces Piece sizes in Figure C2 vary significantly and it may look unfair, but you don't have to worry. Those guests who would like to eat as many sorts of cakes as possible often prefer smaller pieces. Of course, some prefer larger ones. Your mission of this problem is to write a computer program that simulates the cutting process of the cake and reports the size of each piece. Input The input is a sequence of datasets, each of which is of the following format. n w d p1 s1 ... pn sn The first line starts with an integer n that is between 0 and 100 inclusive. It is the number of cuts to be performed. The following w and d in the same line are integers between 1 and 100 inclusive. They denote the width and depth of the cake, respectively. Assume in the sequel that the cake is placed so that w and d are the lengths in the eastwest and northsouth directions, respectively. Each of the following n lines specifies a single cut, cutting one and only one piece into two. pi is an integer between 1 and i inclusive and is the identification number of the piece that is the target of the ith cut. Note that, just before the ith cut, there exist exactly i pieces. Each piece in this stage has a unique identification number that is one of 1, 2, ..., i and is defined as follows: * The earlier a piece was born, the smaller its identification number is. * Of the two pieces born at a time by the same cut, the piece with the smaller area (looking from above) has the smaller identification number. If their areas are the same, you may define as you like the order between them, since your choice in this case has no influence on the final answer. Note that identification numbers are adjusted after each cut. si is an integer between 1 and 1000 inclusive and specifies the starting point of the ith cut. From the northwest corner of the piece whose identification number is pi, you can reach the starting point by traveling si in the clockwise direction around the piece. You may assume that the starting point determined in this way cannot be any one of the four corners of the piece. The ith cut surface is orthogonal to the side face on which the starting point exists. The end of the input is indicated by a line with three zeros. Output For each dataset, print in a line the areas looking from above of all the pieces that exist upon completion of the n cuts specified in the dataset. They should be in ascending order and separated by a space. When multiple pieces have the same area, print it as many times as the number of the pieces. Sample Input 3 5 6 1 18 2 19 1 2 3 4 1 1 1 2 1 3 1 0 2 5 0 0 0 Sample Output 4 4 6 16 1 1 1 1 10
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