Problem:
Score : 300 points

Problem Statement

Iroha is very particular about numbers. There are K digits that she dislikes: D_1, D_2, ..., D_K.

She is shopping, and now paying at the cashier.
Her total is N yen (the currency of Japan), thus she has to hand at least N yen to the cashier (and possibly receive the change).

However, as mentioned before, she is very particular about numbers. When she hands money to the cashier, the decimal notation of the amount must not contain any digits that she dislikes. Under this condition, she will hand the minimum amount of money.

Find the amount of money that she will hand to the cashier.

Constraints

1 ≦ N < 10000

1 ≦ K < 10

0 ≦ D_1 < D_2 < … < D_K≦9

\{D_1,D_2,...,D_K\} ≠ \{1,2,3,4,5,6,7,8,9\}

Input

The input is given from Standard Input in the following format:

N K
D_1 D_2 … D_K

Output

Print the amount of money that Iroha will hand to the cashier.

Sample Input 1

1000 8
1 3 4 5 6 7 8 9

Sample Output 1

2000

She dislikes all digits except 0 and 2.

The smallest integer equal to or greater than N=1000 whose decimal notation contains only 0 and 2, is 2000.

Sample Input 2

9999 1
0

Sample Output 2

9999

Solution in C (Clang 3.8.0) (judge verdict: Accepted)

#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
#include <inttypes.h>
#include <ctype.h>
#include <stdint.h>
#include <string.h>
#include <wchar.h>
#include <math.h>

#define N_MAX (100)
#define P_MAX (100)
#define DP_ARRAY_SIZE (N_MAX * P_MAX / 32 + 1)

#define MIN(a, b) ((a) < (b) ? (a) : (b))
#define MAX(a, b) ((a) > (b) ? (a) : (b))
#define ABS(a) ((a) < 0 ? -(a) : (a))
#define ABSS(a, b) ((a) > (b) ? (a) - (b) : (b) - (a))

int compare_sz_asc(const void* a, const void* b) {
    return *((size_t*)a) < *((size_t*)b) ? -1 : 1;
}

int compare_sz_desc(const void* a, const void* b) {
    return *((size_t*)a) > * ((size_t*)b) ? -1 : 1;
}

int compare_i64_asc(const void* a, const void* b) {
    return *((int64_t*)a) < *((int64_t*)b) ? -1 : 1;
}

int compare_i64_desc(const void* a, const void* b) {
    return *((int64_t*)a) > * ((int64_t*)b) ? -1 : 1;
}

int compare_u64_asc(const void* a, const void* b) {
    return *((uint64_t*)a) < *((uint64_t*)b) ? -1 : 1;
}

int compare_u64_desc(const void* a, const void* b) {
    return *((uint64_t*)a) > * ((uint64_t*)b) ? -1 : 1;
}

int compare_c_asc(const void* a, const void* b) {
    return *((char*)a) < *((char*)b) ? -1 : 1;
}

int compare_c_desc(const void* a, const void* b) {
    return *((char*)a) > * ((char*)b) ? -1 : 1;
}

int compare_dp_asc(const void* a, const void* b) {
    return *((double*)a) < *((double*)b) ? -1 : 1;
}

static size_t powSz(const size_t base, const size_t exp) {
    if (exp == 0) {
        return 1;
    }

    if (exp == 1) {
        return base;
    }

    if (exp % 2 == 0) {
        return powSz(base * base, exp / 2);
    }
    else {
        return base * powSz(base, exp - 1);
    }
}

static size_t comb(const size_t n, const size_t r) {
    size_t result = 1;

    for (size_t i = 0; i < r; i++) {
        result *= n - i;
        result /= i + 1;
    }

    return result;
}

static uint64_t combU64(const uint64_t n, const uint64_t r) {
    uint64_t result = 1;

    for (uint64_t i = 0; i < r; i++) {
        result *= n - i;
        result /= i + 1;
    }

    return result;
}

static size_t gcdZu(size_t m, size_t n) {
    size_t temp;

    while (m % n != 0) {
        temp = n;
        n = m % n;
        m = temp;
    }

    return n;
}

static uint64_t gcdU64(uint64_t m, uint64_t n)
{
    uint64_t temp;

    while (m % n != 0) {
        temp = n;
        n = m % n;
        m = temp;
    }

    return n;
}

typedef struct {
    uint64_t val;
}BHeap_Val;

#define BHEAP_VAL_TYPE BHeap_Val

static int _bHeap_Compare(const BHEAP_VAL_TYPE* parent, const BHEAP_VAL_TYPE* node) {
    return parent->val >= node->val ? -1 : 1;
}

#define BHEAP_INVALID_NODE ((size_t)100000000)

typedef struct {
    BHEAP_VAL_TYPE val;
} BHeap_Node;

static struct {
    size_t size;
    int (*compare)(const BHEAP_VAL_TYPE* parent, const BHEAP_VAL_TYPE* node);
} bHeap_Info;
static BHeap_Node bHeap_Node[1 << 20];

static void bHeap_Init(int(*compare)(const BHEAP_VAL_TYPE* parent, const BHEAP_VAL_TYPE* node)) {
    bHeap_Info.size = 0;
    bHeap_Info.compare = compare;
}

static void bHeap_UpHeap(const size_t nodeIdx) {
    if (nodeIdx == 0) {
        return;
    }

    const size_t parentIdx = (nodeIdx + 1) / 2 - 1;

    const int compareResult = bHeap_Info.compare(&(bHeap_Node[parentIdx].val), &(bHeap_Node[nodeIdx].val));

    if (0 < compareResult) {
        const BHEAP_VAL_TYPE tmp = bHeap_Node[parentIdx].val;
        bHeap_Node[parentIdx].val = bHeap_Node[nodeIdx].val;
        bHeap_Node[nodeIdx].val = tmp;

        if (parentIdx != 0) {
            bHeap_UpHeap(parentIdx);
        }
    }
}

static void bHeap_DownHeap(const size_t nodeIdx) {
    if (bHeap_Info.size - 1 <= nodeIdx) {
        return;
    }

    const size_t leftIdx = 2 * (nodeIdx + 1) - 1;

    if (leftIdx < bHeap_Info.size) {
        const int leftResult = bHeap_Info.compare(&(bHeap_Node[nodeIdx].val), &(bHeap_Node[leftIdx].val));

        size_t swapTarget = leftResult < 0 ? BHEAP_INVALID_NODE : leftIdx;

        const size_t rightIdx = leftIdx + 1;

        if (rightIdx < bHeap_Info.size) {
            const int rightResult = bHeap_Info.compare(&(bHeap_Node[nodeIdx].val), &(bHeap_Node[rightIdx].val));

            if (swapTarget == BHEAP_INVALID_NODE) {
                if (0 < rightResult) {
                    swapTarget = rightIdx;
                }
            }
            else {
                if (0 < rightResult) {
                    const int rightLeftResult = bHeap_Info.compare(&(bHeap_Node[leftIdx].val), &(bHeap_Node[rightIdx].val));

                    if (0 < rightLeftResult) {
                        swapTarget = rightIdx;
                    }
                }
            }
        }

        if (swapTarget != BHEAP_INVALID_NODE) {
            const BHEAP_VAL_TYPE tmp = bHeap_Node[nodeIdx].val;
            bHeap_Node[nodeIdx].val = bHeap_Node[swapTarget].val;
            bHeap_Node[swapTarget].val = tmp;

            bHeap_DownHeap(swapTarget);
        }
    }
}

static void bHeap_Add(const BHEAP_VAL_TYPE val) {
    bHeap_Node[bHeap_Info.size].val = val;

    bHeap_Info.size++;

    bHeap_UpHeap(bHeap_Info.size - 1);
}

static void bHeap_RemoveTop(void) {
    if (bHeap_Info.size == 0) {
        return;
    }

    if (bHeap_Info.size == 1) {
        bHeap_Info.size--;
        return;
    }

    bHeap_Node[0].val = bHeap_Node[bHeap_Info.size - 1].val;

    bHeap_Info.size--;

    bHeap_DownHeap(0);
}

static BHEAP_VAL_TYPE* bHeap_GetTopVal(void) {
    return bHeap_Info.size == 0 ? NULL : &(bHeap_Node[0].val);
}

typedef struct {
    uint64_t cnt;
    size_t* child;
    size_t numChild;
    size_t maxNumChild;
} Tree_Node;

#define TREE_INIT_ALLOC (128)

static Tree_Node tree_Node[200000];

static void tree_Init(const uint64_t N) {
    for (uint64_t i = 0; i < N; i++) {
        tree_Node[i].cnt = 0;
        tree_Node[i].numChild = 0;
        tree_Node[i].child = malloc(sizeof(size_t) * TREE_INIT_ALLOC);
        tree_Node[i].maxNumChild = TREE_INIT_ALLOC;
    }
}

static void tree_AddChild(const size_t parent, const size_t child) {
    if (tree_Node[parent].maxNumChild <= tree_Node[parent].numChild) {
        tree_Node[parent].child = realloc(tree_Node[parent].child, sizeof(size_t) * tree_Node[parent].maxNumChild * 2);
        tree_Node[parent].maxNumChild *= 2;
    }

    tree_Node[parent].child[tree_Node[parent].numChild] = child;
    tree_Node[parent].numChild++;
}

static bool containsDislikeValue(uint64_t val, const uint64_t listSize, const uint64_t* const dislikeList) {
    while (0 < val) {
        const uint64_t digit = val % 10;

        for (uint64_t i = 0; i < listSize; i++) {
            if (digit == dislikeList[i]) {
                return true;
            }
        }

        val /= 10;
    }

    return false;
}

int main(void) {
    uint64_t N, K, D[10];

    scanf("%"PRIu64"%"PRIu64, &N, &K);
    for (uint64_t i = 0; i < K; i++) {
        scanf("%"PRIu64, &D[i]);
    }

    uint64_t payFee = N;

    while (true) {
        if (!containsDislikeValue(payFee, K, D)) {
            break;
        }

        payFee++;
    }

    printf("%"PRIu64"\n", payFee);

    return 0;
}