// LLP single-item knapsack step: lift previous-row values to admit one new item.

class LLPIncrKnapsack {
  int[] LLPIncrKnapsack(int w, int v, int[] C) {
    int[] G = 0;
    forbidden (j) :
      G[j] < C[j] || (j >= w && G[j] < C[j - w] + v)
    =>
      advance :
        G[j] = newValue(j);
    return G;
  }

  // The pointwise maximum of "skip the new item" (C[j]) and
  // "take the new item" (C[j - w] + v, only if j >= w).
  int newValue(int j) {
    int skip = C[j];
    if (j >= w) {
      int take = C[j - w] + v;
      if (take > skip) {
        return take;
      }
    };
    return skip;
  }
}