```
def combinationSum4(self, nums, target):
"""
:type nums: List[int]
:type target: int
:rtype: int
"""
def recCount(startIdx, nums, target, mem):
if target == 0:
return 1
if target < 0:
return 0
if (startIdx, target) in mem:
return mem[(startIdx, target)]
mem[(startIdx, target)] = 0
for i in range(startIdx, startIdx + len(nums)):
# circle the nums array starting from the given startIdx
# not exclude the current num pointed by the startIdx for the next recursion
mem[(startIdx, target)] += recCount(i % len(nums), nums, target - nums[i % len(nums)], mem)
return mem[(startIdx, target)]
# memorize each pair of starting Idx and target
mem = {}
return recCount(0, nums, target, mem)
```
```