13099번 - Cookie Counter 다국어

문제

One day, my grandmas left N cookies. My elder sister and I were going to eat them immediately, but there was the instruction. It said

• Cookies will go bad; you should eat all of them within D days.
• Be careful about overeating; you should eat strictly less than X cookies in a day.

My sister said "How many ways are there to eat all of the cookies? Let's try counting!"

Two ways are considered different if there exists a day such that the numbers of the cookies eaten on that day are different in the two ways. For example, if N, D and X are 5, 2 and 5 respectively, the number of the ways is 4:

• Eating 1 cookie on the first day and 4 cookies on the second day.
• Eating 2 cookies on the first day and 3 cookies on the second day.
• Eating 3 cookies on the first day and 2 cookies on the second day.
• Eating 4 cookies on the first day and 1 cookie on the second day.

I noticed the number of the ways would be very huge and my sister would die before counting it. Therefore, I tried to count it by a computer program to save the life of my sister.

입력

The input consists of multiple datasets. The number of datasets is no more than 100. For each dataset, three numbers N (1 ≤ N ≤ 2,000), D (1 ≤ D ≤ 10¹²) and X (1 ≤ X ≤ 2,000) are written in a line and separated by a space. The end of input is denoted by a line that contains three zeros.

출력

Print the number of the ways modulo 1,000,000,007 in a line for each dataset.

제한

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