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Numbers Combination

Time limit2sMemory limit2048 MB

Summary
Count integer sequences with 1 <= A_i <= i and sum K, modulo 998244353, for N up to 100000 and K up to 200000.
Level

Medium7 of 10

Topics
Combinatorics, Divide and conquer, Math
Solved
No attempts yet

Problem

You are given two integers NN and KK. Count the integer sequences (A1,A2,…,AN)(A_1, A_2, \dots, A_N) that satisfy the following conditions.

  • For every 1≤i≤N1 \le i \le N, 1≤Ai≤i1 \le A_i \le i.
  • A1+A2+⋯+AN=KA_1 + A_2 + \cdots + A_N = K.

Since the answer can be very large, print it modulo 998244353998244353.

Input

Two integers NN and KK are given on one line, where 1≤N≤1000001 \le N \le 100000 and N≤K≤200000N \le K \le 200000.

Output

Print the answer modulo 998244353998244353 on one line.

Examples5

  1. Example 1

    Input
    3 5
    Expected output
    2

  2. Example 2

    Input
    5 6
    Expected output
    4

  3. Example 3

    Input
    7 7
    Expected output
    1

  4. Example 4

    Input
    1 2
    Expected output
    0

  5. Example 5

    Input
    19014 86712
    Expected output
    270258410