You are given a sequence of numbers a1, a2, ..., an, and a number m.

Check if it is possible to choose a non-empty subsequence aij such that the sum of numbers in this subsequence is divisible by m.

Input

The first line contains two numbers, n and m (1 ≤ n ≤ 106, 2 ≤ m ≤ 103) — the size of the original sequence and the number such that sum should be divisible by it.

The second line contains n integers a1, a2, ..., an (0 ≤ ai ≤ 109).

Output

In the single line print either "YES" (without the quotes) if there exists the sought subsequence, or "NO" (without the quotes), if such subsequence doesn't exist.

Examples

Input

3 5
1 2 3


Output

YES


Input

1 6
5


Output

NO


Input

4 6
3 1 1 3


Output

YES


Input

6 6
5 5 5 5 5 5


Output

YES

Note

In the first sample test you can choose numbers 2 and 3, the sum of which is divisible by 5.

In the second sample test the single non-empty subsequence of numbers is a single number 5. Number 5 is not divisible by 6, that is, the sought subsequence doesn't exist.

In the third sample test you need to choose two numbers 3 on the ends.

In the fourth sample test you can take the whole subsequence.
#!/usr/bin/env python
# 577B_modulo.py - Codeforces.com/problemset/problem/577/B by Sergey 2015

import unittest
import sys

###############################################################################
# Modulo Class (Main Program)
###############################################################################


class Modulo:
    """ Modulo representation """

    def __init__(self, test_inputs=None):
        """ Default constructor """

        it = iter(test_inputs.split("\n")) if test_inputs else None

        def uinput():
            return next(it) if it else sys.stdin.readline().rstrip()

        # Reading single elements
        [self.n, self.m] = map(int, uinput().split())

        # Reading a single line of multiple elements
        self.nums = list(map(int, uinput().split()))

        # Modulo
        self.modnums = [v % self.m for v in self.nums]

        # Frequency counter
        self.cnt = {}
        self.vars = {}
        for v in self.modnums:
            if v not in self.cnt.keys():
                self.cnt[v] = 0
                self.vars[v] = []
            self.cnt[v] += 1

    def calculate(self):
        """ Main calcualtion function of the class """

        # For multiples
        for v in self.vars.keys():
            cur = v
            for j in range(self.cnt[v]):
                if j > (v * self.m):
                    break
                self.vars[v].append(cur)
                if cur == 0:
                    return "YES"
                cur = (cur + v) % self.m

        # Collect sum
        cur = set([0])
        for var in self.vars.keys():
            for s in set(cur):
                for v in self.vars[var]:
                    if v == 0:
                        return "YES"
                    res = v + s
                    if res == self.m:
                        return "YES"
                    cur.add(res % self.m)

        return "NO"

###############################################################################
# Unit Tests
###############################################################################


class unitTests(unittest.TestCase):

    def test_single_test(self):
        """ Modulo class testing """

        # Constructor test
        test = "3 5\n1 2 3 3"
        d = Modulo(test)
        self.assertEqual(d.n, 3)
        self.assertEqual(d.m, 5)
        self.assertEqual(d.nums, [1, 2, 3, 3])

        # Sample test
        self.assertEqual(Modulo(test).calculate(), "YES")

        # Sample test
        test = "1 6\n5"
        self.assertEqual(Modulo(test).calculate(), "NO")

        # Sample test
        test = "4 6\n3 1 1 3"
        self.assertEqual(Modulo(test).calculate(), "YES")

        # My tests
        test = "6 6\n5 5 5 5 5 5"
        self.assertEqual(Modulo(test).calculate(), "YES")

        test = "4 5\n1 1 1 1"
        self.assertEqual(Modulo(test).calculate(), "NO")

        # Time limit test
        self.time_limit_test(1000000)

    def time_limit_test(self, nmax):
        """ Timelimit testing """
        import random
        import timeit

        # Random inputs
        test = str(nmax) + " " + str(405) + "\n"
        nums = [random.randint(1, 10000000) for i in range(nmax)]
        test += " ".join(map(str, nums)) + "\n"

        # Run the test
        start = timeit.default_timer()
        d = Modulo(test)
        calc = timeit.default_timer()
        d.calculate()
        stop = timeit.default_timer()
        print("\nTimelimit Test: " +
              "{0:.3f}s (init {1:.3f}s calc {2:.3f}s)".
              format(stop-start, calc-start, stop-calc))

if __name__ == "__main__":

    # Avoiding recursion limitaions
    sys.setrecursionlimit(100000)

    if sys.argv[-1] == "-ut":
        unittest.main(argv=[" "])

    # Print the result string
    sys.stdout.write(Modulo().calculate())
