Construct Target Array With Multiple Sums LeetCode solution in Rust

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type Num = u64;
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use std::collections::BinaryHeap;
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impl Solution {
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  fn preproc(vec: Vec<i32>) -> Vec<Num> {
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    vec.into_iter().map(|e| e as Num).collect::<Vec<_>>()
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  }
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  pub fn is_possible(vec: Vec<i32>) -> bool {
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    let vec = Self::preproc(vec);
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    let mut heap_sum = vec.iter().sum::<Num>();
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    let mut heap = BinaryHeap::from(vec);
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    while let Some(e) = heap.pop() {
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      heap_sum -= e;
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      if e <= heap_sum || heap_sum < 1 {
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        heap.push(e);
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        break;
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      }
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      let mut e_next = e % heap_sum;
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      if e_next < 1 {
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        e_next += heap_sum;
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      }
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      heap_sum += e_next;
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      heap.push(e_next);
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    }
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    heap.into_iter().filter(|&e| e != 1).count() < 1
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  }
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}