__device__ int lowerBound(Particle* particles, int size, int index) {
    int lo = 0, hi = size - 1;
    while (lo < hi) {
        int mid = (lo + hi) / 2;
        if (particles[mid].cell >= index) {
            hi = mid;
        } else {
            lo = mid + 1;
        }
    }
    if (particles[lo].cell == index) {
        return lo;
    }
    return -1;
}