Problem A: Partition 2022 into 10 Distinct Positive Integers

Given the integer \(2022\), determine the number of ways to represent it as a sum of \(10\) distinct positive integers. Two representations are considered identical if they differ only in the order of the summands. For example, \(2022 = 1000 + 1022\) is the same as \(2022 = 1022 + 1000\).

Note: This is a result‐fill problem. You are required to compute the exact result and output it as a single integer.

Mathematically, if \(a_1, a_2,\dots,a_{10}\) are positive integers with \(a_1 < a_2 < \cdots < a_{10}\) and \(a_1+a_2+\cdots+a_{10}=2022\), then output the number of possible solutions. Equivalently, by setting \(b_i=a_i-i\) (so that \(b_i\ge0\) for \(1\le i\le 10\)), you are asked to count the number of non‐decreasing sequences \(b_1\le b_2\le\cdots\le b_{10}\) of nonnegative integers satisfying \[ b_1+b_2+\cdots+b_{10}=2022-\frac{10\cdot11}{2}=1967. \] Any solution which correctly computes the value will be accepted.

inputFormat

There is no input for this problem.

outputFormat

Output a single integer – the number of ways to partition \(2022\) as a sum of \(10\) distinct positive integers.

sample

N/A

335100000000000000