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document.write( "Tom the cat is brushing up his Math skills. He has a bag containing N balls of different colors.
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document.write( "Now Tom can randomly pick any even number of balls from the bag. Tom wants to find out the sum of all such combinations
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document.write( "of balls that he can pull out from the bag. Given he can pull out at max K balls in one pick. \r
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document.write( "Input Format: \r
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document.write( "First line contains two space separated numbers N and K \r
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document.write( "Output Format: \r
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document.write( "The output is the sum of all the combinations of balls he can pull out modulo 10^9+7 i.e. (1000000007)
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document.write( "This writing doesn't make sense.
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document.write( "Besides of it, it seems that formulations of two different problems merged mistakenly in one post here.\r
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document.write( "Actually, there is a beautiful problem close to this formulation.
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document.write( "But it should be cleaned/rectified and reformulated.
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document.write( "Let me do it below.\r
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document.write( " Tom the cat is brushing up his Math skills. He has a bag containing N balls of different colors. (Which means that the balls are distinguishable).\r\n" );
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document.write( " Let N is >= 2.\r\n" );
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document.write( " Now Tom can randomly pick any even number of balls from the bag. Tom wants to find out the 
number \r\n" );
document.write( " of all such combinations of balls that he can pull out from the bag.\r\n" );
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document.write( "OK. Let \"N\" be the number of the balls in the bag.\r\n" );
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document.write( "Then Tom wants to find the number 
, summation over all even m from 0 to N (from 0 to the largest even number lesser or equal to N).\r\n" );
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document.write( "For the solution, let us call this sum as \r\n" );
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= , summation over all even m from 0 to N (from 0 to the largest even number lesser or equal to N).\r\n" );
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document.write( " (index \"e\" is the first letter of the word \"even\").\r\n" );
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document.write( "Also, let us consider another sum, \r\n" );
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= 
, summation over all odd k from 0 to N (from zero to the largest odd number lesser or equal to N).\r\n" );
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document.write( " (index \"o\" is the first letter of the word \"odd\").\r\n" );
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document.write( "Then these two equalities are true:\r\n" );
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document.write( "1) + = 
, (1) and\r\n" );
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document.write( "2) = . (2)\r\n" );
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document.write( "Equality (1) is true, because its left side is the sum of all binomial coefficients of the binomial expansion 
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document.write( "Then (1) is well known property of the sum of the binomial coefficients of the binomial expansion\r\n" );
document.write( "(see the lesson The Pascal's triangle in this site).\r\n" );
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document.write( "The property (2) is also well known. It is read as \"the alternate sum of the binomial coefficients is equal to zero\"\r\n" );
document.write( "and in this form it is also proved in the referred lesson.\r\n" );
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document.write( "Fantastic! Now from (1) and (2) we have = = 
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document.write( "This is the solution, the result and the answer for the curious Tom the cat,\r\n" );
document.write( "and this is the solution of the problem: The number under the question is equal to .\r\n" );
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document.write( "Isn't it a beautiful problem / solution / result ?\r\n" );
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document.write( "![\"\"](\"/images/stars/stars-13.gif\")
