CF754D.Fedor and coupons

All our characters have hobbies. The same is true for Fedor. He enjoys shopping in the neighboring supermarket.

The goods in the supermarket have unique integer ids. Also, for every integer there is a product with id equal to this integer. Fedor has n discount coupons, the i-th of them can be used with products with ids ranging from l__i to r__i, inclusive. Today Fedor wants to take exactly k coupons with him.

Fedor wants to choose the k coupons in such a way that the number of such products x that all coupons can be used with this product x is as large as possible (for better understanding, see examples). Fedor wants to save his time as well, so he asks you to choose coupons for him. Help Fedor!

我们所有的角色都有各自的爱好，费多尔也不例外。他喜欢在附近的超市购物。

超市中的商品具有唯一的整数编号。此外，对于每个整数，都存在一个编号恰好等于该整数的商品。费多尔有 $n$ 张折扣券，其中第 $i$ 张折扣券可用于编号在区间 $[l_i, r_i]$ 内（含端点）的所有商品。今天费多尔想恰好带 $k$ 张折扣券出门。

费多尔希望选择 $k$ 张折扣券，使得满足“所有这 $k$ 张折扣券均能用于该商品”的商品编号 $x$ 的个数尽可能多（为便于理解，请参见示例）。费多尔还想节省时间，因此请你帮他选出这些折扣券。请帮助费多尔！

The first line contains two integers n and k (1 ≤ k ≤ n ≤ 3·105) — the number of coupons Fedor has, and the number of coupons he wants to choose.

Each of the next n lines contains two integers l__i and r__i ( - 109 ≤ l__i ≤ r__i ≤ 109) — the description of the i-th coupon. The coupons can be equal.

第一行包含两个整数 $n$ 和 $k$（$1 ≤ k ≤ n ≤ 3·10^5$）—— 分别表示 Fedor 拥有的优惠券数量，以及他想要选择的优惠券数量。

接下来的 $n$ 行中，每行包含两个整数 $l_i$ 和 $r_i$（$-10^9 ≤ l_i ≤ r_i ≤ 10^9$）—— 描述第 $i$ 张优惠券。优惠券可以相同。

In the first line print single integer — the maximum number of products with which all the chosen coupons can be used. The products with which at least one coupon cannot be used shouldn't be counted.

In the second line print k distinct integers _p_1, _p_2, ..., p__k (1 ≤ p__i ≤ n) — the ids of the coupons which Fedor should choose.

If there are multiple answers, print any of them.

第一行输出一个整数——所有被选中的优惠券均可使用的最大商品数量。至少有一个优惠券无法使用的产品不应计入。

第二行输出 $k$ 个互不相同的整数 $p_1,\,p_2,\,...,\,p_k$（其中 $1\le p_i\le n$）——Fedor 应当选择的优惠券编号。

若存在多个答案，输出任意一个即可。

In the first example if we take the first two coupons then all the products with ids in range [40, 70] can be bought with both coupons. There are 31 products in total.

In the second example, no product can be bought with two coupons, that is why the answer is 0. Fedor can choose any two coupons in this example.

在第一个例子中，如果我们选择前两张优惠券，则所有编号在区间 [40, 70] 内的产品均可使用这两张优惠券购买。总共有 31 个产品。

在第二个例子中，没有任何产品能同时使用两张优惠券购买，因此答案为 0。在此例中，Fedor 可以任意选择两张优惠券。