```typescript
export function stampTable(dies: [string, number][]): Map<string, number> {
  const table = new Map<string, number>();
  for (const [fragment, price] of dies) {
    if (typeof fragment !== "string" || fragment.length === 0) {
      throw new Error("a die fragment must be a non-empty string");
    }
    if (!Number.isInteger(price) || price <= 0) {
      throw new Error("a die price must be a positive integer");
    }
    if (table.has(fragment)) {
      throw new Error("die listed twice: " + fragment);
    }
    table.set(fragment, price);
  }
  return table;
}

export function stampCover(label: string, dies: [string, number][]): number {
  if (typeof label !== "string" || label.length === 0) {
    throw new Error("the label must be a non-empty string");
  }

  const table = stampTable(dies);

  // Create an array to keep track of the minimum cost to make up each prefix of the label
  const minCosts: number[] = [];
  minCosts[0] = 0;

  for (let i = 1; i <= label.length; i++) {
    let minCostForLabelI = Infinity;
    for (const fragment of table.keys()) {
      if (label.startsWith(fragment, i - fragment.length)) {
        const cost = table.get(fragment)! + (i - fragment.length);
        minCostForLabelI = Math.min(minCostForLabelI, cost);
      }
    }

    // If no valid sequence exists for the current prefix, set it to Infinity
    if (minCostForLabelI === Infinity) {
      throw new Error("no sequence of dies can spell the label");
    }

    minCosts.push(minCostForLabelI);
  }

  return minCosts[label.length];
}
```