#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>

#define MAX_SIZE 1000

struct Entry {
    int remainder;
    int index;
    bool used;
};

bool solution(int* nums, int numsSize, int k) {
    struct Entry remainderMap[MAX_SIZE];
    for (int i = 0; i < MAX_SIZE; i++) {
        remainderMap[i].used = false;
    }
    
    // Add initial entry for remainder 0
    remainderMap[0].remainder = 0;
    remainderMap[0].index = -1;
    remainderMap[0].used = true;
    
    int prefixSum = 0;
    
    for (int i = 0; i < numsSize; i++) {
        prefixSum += nums[i];
        int remainder = prefixSum % k;
        if (remainder < 0) remainder += k;
        
        // Check if remainder exists
        for (int j = 0; j < MAX_SIZE; j++) {
            if (remainderMap[j].used && remainderMap[j].remainder == remainder) {
                if (i - remainderMap[j].index > 1) {
                    return true;
                }
                goto next_iteration;
            }
        }
        
        // Add new remainder
        for (int j = 0; j < MAX_SIZE; j++) {
            if (!remainderMap[j].used) {
                remainderMap[j].remainder = remainder;
                remainderMap[j].index = i;
                remainderMap[j].used = true;
                break;
            }
        }
        
        next_iteration:;
    }
    
    return false;
}

int main() {
    char line[1000];
    fgets(line, sizeof(line), stdin);
    
    // Parse array
    int nums[1000];
    int numsSize = 0;
    char* token = strtok(line + 1, ",]");
    while (token != NULL) {
        nums[numsSize++] = atoi(token);
        token = strtok(NULL, ",]");
    }
    
    int k;
    scanf("%d", &k);
    
    bool result = solution(nums, numsSize, k);
    printf(result ? "true\n" : "false\n");
    return 0;
}